Diffusion Language models

Diffusion language models offer unique benefits over autoregressive models due to their potential for parallelized generation and controllability, yet they lag in likelihood modeling and are limited to fixed-length generation. In this work, we introduce a class of block diffusion language models that interpolate between discrete denoising diffusion and autoregressive models. Block diffusion overcomes key limitations of both approaches by supporting flexible-length generation and improving inference efficiency with KV caching and parallel token sampling. We propose a recipe for building effective block diffusion models that includes an efficient training algorithm, estimators of gradient variance, and data-driven noise schedules to minimize the variance. Block diffusion sets a new state-of-the-art performance among diffusion models on language modeling benchmarks and enables generation of arbitrary-length sequences. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/bd3lms.

While diffusion models excel at generating high-quality images, prior work reports a significant performance gap between diffusion and autoregressive (AR) methods in language modeling. In this work, we show that simple masked discrete diffusion is more performant than previously thought. We apply an effective training recipe that improves the performance of masked diffusion models and derive a simplified, Rao-Blackwellized objective that results in additional improvements. Our objective has a simple form -- it is a mixture of classical masked language modeling losses -- and can be used to train encoder-only language models that admit efficient samplers, including ones that can generate arbitrary lengths of text semi-autoregressively like a traditional language model. On language modeling benchmarks, a range of masked diffusion models trained with modern engineering practices achieves a new state-of-the-art among diffusion models, and approaches AR perplexity. We provide the code, along with a blog post and video tutorial on the project page: https://s-sahoo.com/mdlm

We introduce MMaDA, a novel class of multimodal diffusion foundation models designed to achieve superior performance across diverse domains such as textual reasoning, multimodal understanding, and text-to-image generation. The approach is distinguished by three key innovations: (i) MMaDA adopts a unified diffusion architecture with a shared probabilistic formulation and a modality-agnostic design, eliminating the need for modality-specific components. This architecture ensures seamless integration and processing across different data types. (ii) We implement a mixed long chain-of-thought (CoT) fine-tuning strategy that curates a unified CoT format across modalities. By aligning reasoning processes between textual and visual domains, this strategy facilitates cold-start training for the final reinforcement learning (RL) stage, thereby enhancing the model's ability to handle complex tasks from the outset. (iii) We propose UniGRPO, a unified policy-gradient-based RL algorithm specifically tailored for diffusion foundation models. Utilizing diversified reward modeling, UniGRPO unifies post-training across both reasoning and generation tasks, ensuring consistent performance improvements. Experimental results demonstrate that MMaDA-8B exhibits strong generalization capabilities as a unified multimodal foundation model. It surpasses powerful models like LLaMA-3-7B and Qwen2-7B in textual reasoning, outperforms Show-o and SEED-X in multimodal understanding, and excels over SDXL and Janus in text-to-image generation. These achievements highlight MMaDA's effectiveness in bridging the gap between pretraining and post-training within unified diffusion architectures, providing a comprehensive framework for future research and development. We open-source our code and trained models at: https://github.com/Gen-Verse/MMaDA

Diffusion Language Models (DLMs) have been seen as a promising competitor for autoregressive language models. However, diffusion language models have long been constrained by slow inference. A core challenge is that their non-autoregressive architecture and bidirectional attention preclude the key-value cache that accelerates decoding. We address this bottleneck by proposing a KV-cache-like mechanism, delayed KV-Cache, for the denoising process of DLMs. Our approach is motivated by the observation that different tokens have distinct representation dynamics throughout the diffusion process. Accordingly, we propose a delayed and conditioned caching strategy for key and value states. We design two complementary variants to cache key and value step-by-step: (1) dKV-Cache-Decode, which provides almost lossless acceleration, and even improves performance on long sequences, suggesting that existing DLMs may under-utilise contextual information during inference. (2) dKV-Cache-Greedy, which has aggressive caching with reduced lifespan, achieving higher speed-ups with quadratic time complexity at the cost of some performance degradation. dKV-Cache, in final, achieves from 2-10x speedup in inference, largely narrowing the gap between ARs and DLMs. We evaluate our dKV-Cache on several benchmarks, delivering acceleration across general language understanding, mathematical, and code-generation benchmarks. Experiments demonstrate that cache can also be used in DLMs, even in a training-free manner from current DLMs.

We introduce the Diffusion Chain of Lateral Thought (DCoLT), a reasoning framework for diffusion language models. DCoLT treats each intermediate step in the reverse diffusion process as a latent"thinking"action and optimizes the entire reasoning trajectory to maximize the reward on the correctness of the final answer with outcome-based Reinforcement Learning (RL). Unlike traditional Chain-of-Thought (CoT) methods that follow a causal, linear thinking process, DCoLT allows bidirectional, non-linear reasoning with no strict rule on grammatical correctness amid its intermediate steps of thought. We implement DCoLT on two representative Diffusion Language Models (DLMs). First, we choose SEDD as a representative continuous-time discrete diffusion model, where its concrete score derives a probabilistic policy to maximize the RL reward over the entire sequence of intermediate diffusion steps. We further consider the discrete-time masked diffusion language model -- LLaDA, and find that the order to predict and unmask tokens plays an essential role to optimize its RL action resulting from the ranking-based Unmasking Policy Module (UPM) defined by the Plackett-Luce model. Experiments on both math and code generation tasks show that using only public data and 16 H800 GPUs, DCoLT-reinforced DLMs outperform other DLMs trained by SFT or RL or even both. Notably, DCoLT-reinforced LLaDA boosts its reasoning accuracy by +9.8%, +5.7%, +11.4%, +19.5% on GSM8K, MATH, MBPP, and HumanEval.

This paper presents LLaDA2.0 -- a tuple of discrete diffusion large language models (dLLM) scaling up to 100B total parameters through systematic conversion from auto-regressive (AR) models -- establishing a new paradigm for frontier-scale deployment. Instead of costly training from scratch, LLaDA2.0 upholds knowledge inheritance, progressive adaption and efficiency-aware design principle, and seamless converts a pre-trained AR model into dLLM with a novel 3-phase block-level WSD based training scheme: progressive increasing block-size in block diffusion (warm-up), large-scale full-sequence diffusion (stable) and reverting back to compact-size block diffusion (decay). Along with post-training alignment with SFT and DPO, we obtain LLaDA2.0-mini (16B) and LLaDA2.0-flash (100B), two instruction-tuned Mixture-of-Experts (MoE) variants optimized for practical deployment. By preserving the advantages of parallel decoding, these models deliver superior performance and efficiency at the frontier scale. Both models were open-sourced.

Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging. Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models. Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts. We release a suite of DLMs (127M-355M-7B) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions https://github.com/HKUNLP/DiffuLLaMA.

Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high quality outputs. In this work, we highlight and leverage an overlooked property of DLMs early answer convergence: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random remasking schedules. For example, on GSM8K and MMLU, up to 97% and 99% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce Prophet, a training-free fast decoding paradigm that enables early commit decoding. Specifically, Prophet dynamically decides whether to continue refinement or to go"all-in"(i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4x while preserving high generation quality. These results recast DLM decoding as a problem of when to stop sampling, and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is publicly available at https://github.com/pixeli99/Prophet.

Improving the reasoning capabilities of diffusion-based large language models (dLLMs) through reinforcement learning (RL) remains an open problem. The intractability of dLLMs likelihood function necessitates approximating the current, old, and reference policy likelihoods at each policy optimization step. This reliance introduces additional computational overhead, and can lead to large variance and estimation error in RL objective -- particularly in computing the policy ratio for importance sampling. To mitigate these issues, we introduce wd1, a novel ratio-free policy optimization approach that reformulates the RL objective as a weighted log-likelihood, requiring only a single approximation for the current parametrized policy likelihood. We formally show that our proposed method can be interpreted as energy-guided discrete diffusion training combined with negative sample unlearning, thereby confirming its theoretical soundness. In experiments on LLaDA-8B model, wd1 outperforms diffusion-based GRPO (d1) while requiring lower computational cost, achieving up to a $+59\%$ improvement in accuracy. Furthermore, we extend wd1 to denoising-stepwise weighted policy optimization (wd1++), achieving state-of-the-art math performance of $44.2\%$ on MATH500 and $84.5\%$ on GSM8K with only 20 RL training steps.

Under strictly controlled pre-training settings, we observe a Crossover: when unique data is limited, diffusion language models (DLMs) consistently surpass autoregressive (AR) models by training for more epochs. The crossover shifts later with more or higher-quality data, earlier with larger models, and persists across dense and sparse architectures. We attribute the gains to three compounding factors: (1) any-order modeling, (2) super-dense compute from iterative bidirectional denoising, and (3) built-in Monte Carlo augmentation; input or parameter noise improves AR under data constraint but cannot close the gap. At scale, a 1.7B DLM trained with a ~1.5T-token compute budget on 10B unique Python tokens overtakes an AR coder trained with strictly matched settings. In addition, a 1B-parameter DLM achieves>56% accuracy on HellaSwag and>33% on MMLU using only 1B tokens, without any special tricks, just by repeating standard pre-training data. We also show that rising validation cross-entropy does not imply degraded downstream performance in this regime.

Masked diffusion language models (MDLM) have shown strong promise for non-autoregressive text generation, yet existing samplers act as implicit planners, selecting tokens to unmask via denoiser confidence or entropy scores. Such heuristics falter under parallel unmasking - they ignore pairwise interactions between tokens and cannot account for dependencies when unmasking multiple positions at once, limiting their inference time to traditional auto-regressive (AR) models. We introduce the Dilated-scheduled Unmasking Strategy (DUS), an inference-only, planner-model-free method that requires no additional training. DUS leverages a first-order Markov assumption to partition sequence positions into dilation-based groups of non-adjacent tokens, enabling independent, parallel unmasking steps that respect local context that minimizes the joint entropy of each iteration step. Unlike semi-AR block approaches (e.g., LLADA and Dream) that still invoke the denoiser per block, DUS reduces the number of denoiser calls to O(log B) per generation block - yielding substantial speedup over the O(B) run time of state-of-the-art diffusion models, where B is the block size in the semi-AR inference process. In experiments on math (GSM8K) and code completion (Humaneval, MBPP) benchmarks - domains suited to non-ordinal generation - DUS improves scores over parallel confidence-based planner, without modifying the underlying denoiser. DUS offers a lightweight, budget-aware approach to efficient, high-quality text generation, paving the way to unlock the true capabilities of MDLMs.

While diffusion language models (DLMs) have achieved competitive performance in text generation, improving their reasoning ability with reinforcement learning remains an active research area. Here, we introduce d2, a reasoning framework tailored for masked DLMs. Central to our framework is a new policy gradient algorithm that relies on accurate estimates of the sampling trajectory likelihoods. Our likelihood estimator, d2-AnyOrder, achieves exact trajectory likelihood with a single model pass for DLMs that support a sampling algorithm called any-order decoding. Through an empirical study of widely used DLMs, we show that any-order decoding is not universally supported in practice. Consequently, for DLMs that do not naturally support any-order decoding, we propose another estimator, d2-StepMerge, which, unlike d2-AnyOrder, only approximates the trajectory likelihood. d2-StepMerge trades off compute for approximation accuracy in an analytically tractable manner. Empirically, d2 significantly outperforms widely-used RL baselines when applied to popular DLMs, and sets a new state-of-the-art performance for DLMs on logical reasoning tasks (Countdown and Sudoku) and math reasoning benchmarks (GSM8K and MATH500). We provide the code along with a blog post on the project page: https://guanghanwang.com/d2

We introduce Quokka, the first systematic scaling law for diffusion language models (DLMs), encompassing both compute-constrained and data-constrained regimes, and studying the key modeling and optimization designs. Quokka is a good friend of Chinchilla and provides wider scopes. We hope the results would bring short-term practical guidance in DLMs training and long-term inspirations for the whole AI community.

Diffusion-based Large Language Models (dLLMs) parallelize text generation by framing decoding as a denoising process, but suffer from high computational overhead since they predict all future suffix tokens at each step while retaining only a small fraction. We propose Diffusion Scratchpad (DPad), a training-free method that restricts attention to a small set of nearby suffix tokens, preserving fidelity while eliminating redundancy. DPad integrates two strategies: (i) a sliding window, which maintains a fixed-length suffix window, and (ii) distance-decay dropout, which deterministically removes distant suffix tokens before attention computation. This simple design is compatible with existing optimizations such as prefix caching and can be implemented with only a few lines of code. Comprehensive evaluations across multiple benchmarks on LLaDA-1.5 and Dream models demonstrate that DPad delivers up to $\mathbf{61.4\times}$ speedup over vanilla dLLMs while maintaining comparable accuracy, highlighting its potential for efficient and scalable long-sequence inference. Our code is available at https://github.com/Crys-Chen/DPad.

Diffusion large language models (dLLMs) are emerging as an efficient alternative to autoregressive models due to their ability to decode multiple tokens in parallel. However, aligning dLLMs with human preferences or task-specific rewards via reinforcement learning (RL) is challenging because their intractable log-likelihood precludes the direct application of standard policy gradient methods. While prior work uses surrogates like the evidence lower bound (ELBO), these one-sided approximations can introduce significant policy gradient bias. To address this, we propose the Sandwiched Policy Gradient (SPG) that leverages both an upper and a lower bound of the true log-likelihood. Experiments show that SPG significantly outperforms baselines based on ELBO or one-step estimation. Specifically, SPG improves the accuracy over state-of-the-art RL methods for dLLMs by 3.6% in GSM8K, 2.6% in MATH500, 18.4% in Countdown and 27.0% in Sudoku.

Discrete diffusion models have recently emerged as strong alternatives to autoregressive language models, matching their performance through large-scale training. However, inference-time control remains relatively underexplored. In this work, we study how to steer generation toward desired rewards without retraining the models. Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement. We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity under reward optimization. PG-DLM constructs a Markov chain over full denoising trajectories and applies a conditional sequential Monte Carlo kernel to resample them. We derive theoretical guarantees for convergence, including asymptotic consistency and variance bounds. Within this framework, we further analyze trade-offs across four key axes for inference-time scaling under fixed budgets: iterations, samples, denoising steps, and reward estimation. Our analysis shows scaling iterations achieves the best reward-perplexity trade-off. Empirically, PG-DLM consistently outperforms prior methods using MDLM and LLaDA-8B as base models across a wide range of compute budgets for reward-guided generation tasks including toxicity and sentiment control as well as linguistic acceptability.

Diffusion large language models (dLLMs) generate text through iterative denoising, yet current decoding strategies discard rich intermediate predictions in favor of the final output. Our work here reveals a critical phenomenon, temporal oscillation, where correct answers often emerge in the middle process, but are overwritten in later denoising steps. To address this issue, we introduce two complementary methods that exploit temporal consistency: 1) Temporal Self-Consistency Voting, a training-free, test-time decoding strategy that aggregates predictions across denoising steps to select the most consistent output; and 2) a post-training method termed Temporal Consistency Reinforcement, which uses Temporal Semantic Entropy (TSE), a measure of semantic stability across intermediate predictions, as a reward signal to encourage stable generations. Empirical results across multiple benchmarks demonstrate the effectiveness of our approach. Using the negative TSE reward alone, we observe a remarkable average improvement of 24.7% on the Countdown dataset over an existing dLLM. Combined with the accuracy reward, we achieve absolute gains of 2.0% on GSM8K, 4.3% on MATH500, 6.6% on SVAMP, and 25.3% on Countdown, respectively. Our findings underscore the untapped potential of temporal dynamics in dLLMs and offer two simple yet effective tools to harness them.

Diffusion-based large language models (dLLMs) have emerged as a promising alternative to autoregressive (AR) LLMs, leveraging denoising-based generation to enable inherent parallelism. Even more and more open-sourced dLLM models emerge, yet their widespread adoption remains constrained by the lack of a standardized and efficient inference framework. We present dInfer, an efficient and extensible framework for dLLM inference. dInfer decomposes the inference pipeline into four modular components--model, diffusion iteration manager, decoding strategy, and KV-cache manager--and integrates novel algorithms for each component alongside system-level optimizations. Through this combination of algorithmic innovations and system enhancements, dInfer achieves substantial efficiency gains without compromising output quality on LLaDA-MoE. At batch size 1, it surpasses 1,100 tokens per second on HumanEval and averages over 800 tokens per second across six benchmarks on $8\times$ H800 GPUs. Compared to prior systems, dInfer delivers a $10\times$ speedup over Fast-dLLM while maintaining similar model performance. Even compared to the AR model (with a comparable number of activation parameters and performance) QWen2.5-3B, which is highly optimized with the latest vLLM inference engine, dInfer still delivers a $2$-$3\times$ speedup. The implementation of dInfer is open-sourced at https://github.com/inclusionAI/dInfer.

Mask-based Diffusion Language Models (DLMs) struggle to revise incorrect tokens: once a token is generated, it typically remains fixed. The key challenge is to identify potential errors in the inputs. In this paper, we propose \emph{\underline{Rem}asking-\underline{e}nabled \underline{Di}ffusion Language Model (RemeDi}, a mask-based DLM that introduces \emph{remasking} as another fundamental mechanism, enabling more flexible text refinement in diffusion-based text generation. To achieve this, RemeDi jointly predicts token distributions and per-token confidence scores at each step. The confidence scores determine which tokens to be unmasked after the current step, allowing the model to identify tokens with low quality and remask them. These remasked tokens can be resampled with richer context in subsequent steps. We design a remask-aware pipeline to train this ability, including supervised fine-tuning which teaches the model to detect and remask incorrect tokens in addition to predict mask tokens, and reinforcement learning which optimizes full generation trajectories toward higher rewards. Experiments show that RemeDi achieves the state-of-the-art results among open-source DLMs on multiple datasets.

Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have recently emerged as a promising alternative. Unfortunately, these models still underperform the autoregressive counterparts, with the performance gap increasing when reducing the number of sampling steps. Our analysis reveals that this degradation is a consequence of an imperfect approximation used by diffusion models. In this work, we propose Energy-based Diffusion Language Model (EDLM), an energy-based model operating at the full sequence level for each diffusion step, introduced to improve the underlying approximation used by diffusion models. More specifically, we introduce an EBM in a residual form, and show that its parameters can be obtained by leveraging a pretrained autoregressive model or by finetuning a bidirectional transformer via noise contrastive estimation. We also propose an efficient generation algorithm via parallel important sampling. Comprehensive experiments on language modeling benchmarks show that our model can consistently outperform state-of-the-art diffusion models by a significant margin, and approaches autoregressive models' perplexity. We further show that, without any generation performance drop, our framework offers a 1.3$\times$ sampling speedup over existing diffusion models. Reproduced code is available at https://github.com/MinkaiXu/Energy-Diffusion-LLM.

Diffusion language models, as a promising alternative to traditional autoregressive (AR) models, enable faster generation and richer conditioning on bidirectional context. However, they suffer from a key discrepancy between training and inference: during inference, MDLMs progressively reveal the structure of the generated sequence by producing fewer and fewer masked tokens, whereas this structure is ignored in training as tokens are masked at random. Although this discrepancy between training and inference can lead to suboptimal performance, it has been largely overlooked by previous works, leaving closing this gap between the two stages an open problem. To address this, we frame the problem of learning effective denoising trajectories as a sequential decision-making problem and use the resulting framework to apply reinforcement learning. We propose a novel Masked Diffusion Policy Optimization (MDPO) to exploit the Markov property diffusion possesses and explicitly train the model under the same progressive refining schedule used at inference. MDPO matches the performance of the previous state-of-the-art (SOTA) method with 60x fewer gradient updates, while achieving average improvements of 9.6% on MATH500 and 54.2% on Countdown over SOTA when trained within the same number of weight updates. Additionally, we improve the remasking strategy of MDLMs as a plug-in inference replacement to overcome the limitation that the model cannot refine tokens flexibly. This training-free method, termed Running Confidence Remasking (RCR), consistently enhances performance and provides further improvements when used with MDPO. Our findings establish great potential for investigating the discrepancy between pre-training and inference of MDLMs. Code: https://github.com/autonomousvision/mdpo. Project Page: https://cli212.github.io/MDPO/.

Autoregressive (AR) generation is the standard decoding paradigm for Large Language Models (LLMs), but its token-by-token nature limits parallelism at inference time. Diffusion Language Models (DLLMs) offer parallel decoding by recovering multiple masked tokens per step; however, in practice they often fail to translate this parallelism into deployment speed gains over optimized AR engines (e.g., vLLM). A key reason is that many DLLMs rely on bidirectional attention, which breaks standard prefix KV caching and forces repeated contextualization, undermining efficiency. We propose WeDLM, a diffusion decoding framework built entirely on standard causal attention to make parallel generation prefix-cache friendly. The core idea is to let each masked position condition on all currently observed tokens while keeping a strict causal mask, achieved by Topological Reordering that moves observed tokens to the physical prefix while preserving their logical positions. Building on this property, we introduce a streaming decoding procedure that continuously commits confident tokens into a growing left-to-right prefix and maintains a fixed parallel workload, avoiding the stop-and-wait behavior common in block diffusion methods. Experiments show that WeDLM preserves the quality of strong AR backbones while delivering substantial speedups, approaching 3x on challenging reasoning benchmarks and up to 10x in low-entropy generation regimes; critically, our comparisons are against AR baselines served by vLLM under matched deployment settings, demonstrating that diffusion-style decoding can outperform an optimized AR engine in practice.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Although autoregressive models have dominated language modeling in recent years, there has been a growing interest in exploring alternative paradigms to the conventional next-token prediction framework. Diffusion-based language models have emerged as a compelling alternative due to their powerful parallel generation capabilities and inherent editability. However, these models are often constrained by fixed-length generation. A promising direction is to combine the strengths of both paradigms, segmenting sequences into blocks, modeling autoregressive dependencies across blocks while leveraging discrete diffusion to estimate the conditional distribution within each block given the preceding context. Nevertheless, their practical application is often hindered by two key limitations: rigid fixed-length outputs and a lack of flexible control mechanisms. In this work, we address the critical limitations of fixed granularity and weak controllability in current large diffusion language models. We propose CtrlDiff, a dynamic and controllable semi-autoregressive framework that adaptively determines the size of each generation block based on local semantics using reinforcement learning. Furthermore, we introduce a classifier-guided control mechanism tailored to discrete diffusion, which significantly reduces computational overhead while facilitating efficient post-hoc conditioning without retraining. Extensive experiments demonstrate that CtrlDiff sets a new standard among hybrid diffusion models, narrows the performance gap to state-of-the-art autoregressive approaches, and enables effective conditional text generation across diverse tasks.

This paper introduces diffusion protein language model (DPLM), a versatile protein language model that demonstrates strong generative and predictive capabilities for protein sequences. We first pre-train scalable DPLMs from evolutionary-scale protein sequences within a generative self-supervised discrete diffusion probabilistic framework, which generalizes language modeling for proteins in a principled way. After pre-training, DPLM exhibits the ability to generate structurally plausible, novel, and diverse protein sequences for unconditional generation. We further demonstrate the proposed diffusion generative pre-training makes DPLM possess a better understanding of proteins, making it a superior representation learner, which can be fine-tuned for various predictive tasks, comparing favorably to ESM2 (Lin et al., 2022). Moreover, DPLM can be tailored for various needs, which showcases its prowess of conditional generation in several ways: (1) conditioning on partial peptide sequences, e.g., generating scaffolds for functional motifs with high success rate; (2) incorporating other modalities as conditioner, e.g., structure-conditioned generation for inverse folding; and (3) steering sequence generation towards desired properties, e.g., satisfying specified secondary structures, through a plug-and-play classifier guidance. Code is released at \url{https://github.com/bytedance/dplm}.

Diffusion language models (DLMs) have strong theoretical efficiency but are limited by fixed-length decoding and incompatibility with key-value (KV) caches. Block diffusion mitigates these issues, yet still enforces a fixed block size and requires expensive training. We introduce Next Sequence Prediction (NSP), which unifies next-token and next-block prediction, enabling the model to adaptively determine the generation length at each step. When the length is fixed to 1, NSP reduces to standard next-token prediction. Building on NSP, we propose Sequential Diffusion Language Model (SDLM), which can retrofit pre-trained autoregressive language models (ALMs) at minimal cost. Specifically, SDLM performs diffusion inference within fixed-size mask blocks, but dynamically decodes consecutive subsequences based on model confidence, thereby preserving KV-cache compatibility and improving robustness to varying uncertainty and semantics across the sequence. Experiments show that SDLM matches or surpasses strong autoregressive baselines using only 3.5M training samples, while achieving 2.1 higher throughput than Qwen-2.5. Notably, the SDLM-32B model delivers even more pronounced efficiency gains, demonstrating the strong scalability potential of our modeling paradigm. Project page and codes: https://github.com/OpenGVLab/SDLM

This paper introduces DLM-One, a score-distillation-based framework for one-step sequence generation with continuous diffusion language models (DLMs). DLM-One eliminates the need for iterative refinement by aligning the scores of a student model's outputs in the continuous token embedding space with the score function of a pretrained teacher DLM. We investigate whether DLM-One can achieve substantial gains in sampling efficiency for language modeling. Through comprehensive experiments on DiffuSeq -- a representative continuous DLM -- we show that DLM-One achieves up to ~500x speedup in inference time while maintaining competitive performance on benchmark text generation tasks used to evaluate the teacher models. We further analyze the method's empirical behavior across multiple datasets, providing initial insights into its generality and practical applicability. Our findings position one-step diffusion as a promising direction for efficient, high-quality language generation and broader adoption of continuous diffusion models operating in embedding space for natural language processing.

While diffusion language models (DLMs) offer a promising alternative to autoregressive models (ARs), existing open-source DLMs suffer from high inference latency. This bottleneck is mainly due to the attention's quadratic complexity with respect to context length in computing all query-key pairs. Intuitively, to reduce this complexity, a natural strategy is to restrict attention to sparse patterns that retain only the most relevant connections. Such approaches are well-established in ARs, where attention follows fixed and clearly defined sparse patterns. However, in DLMs, we observe distinct sparsity behaviors: (1) attention patterns vary across heads, (2) attention patterns in each head remain highly similar across denoising steps, and (3) early denoising steps are critical for generation. These findings render sparse attention methods designed for ARs largely incompatible with DLMs, as they fail to capture head-specific structures and risk degrading generation when applied in early denoising steps. To address these challenges, we propose SparseD, a novel sparse attention method for DLMs. Leveraging the observations, SparseD only requires pre-computing head-specific sparse patterns one time, and reuses them across all steps. This prevents recomputing sparse patterns at each denoising step. Meanwhile, SparseD uses full attention in the early steps, then switches to sparse attention later to maintain generation quality. Together, these establish SparseD as a practical and efficient solution for deploying DLMs in long-context applications. Experimental results demonstrate that SparseD achieves lossless acceleration, delivering up to $1.50\times$ speedup over FlashAttention at a 64k context length with 1,024 denoising steps.

Diffusion language models (DLMs) enable parallel, order-agnostic generation with iterative refinement, offering a flexible alternative to autoregressive large language models (LLMs). However, adapting reinforcement learning (RL) fine-tuning to DLMs remains an open challenge because of the intractable likelihood. Pioneering work such as diffu-GRPO estimated token-level likelihoods via one-step unmasking. While computationally efficient, this approach is severely biased. A more principled foundation lies in sequence-level likelihoods, where the evidence lower bound (ELBO) serves as a surrogate. Yet, despite this clean mathematical connection, ELBO-based methods have seen limited adoption due to the prohibitive cost of likelihood evaluation. In this work, we revisit ELBO estimation and disentangle its sources of variance. This decomposition motivates reducing variance through fast, deterministic integral approximations along a few pivotal dimensions. Building on this insight, we introduce Group Diffusion Policy Optimization (GDPO), a new RL algorithm tailored for DLMs. GDPO leverages simple yet effective Semi-deterministic Monte Carlo schemes to mitigate the variance explosion of ELBO estimators under vanilla double Monte Carlo sampling, yielding a provably lower-variance estimator under tight evaluation budgets. Empirically, GDPO achieves consistent gains over pretrained checkpoints and outperforms diffu-GRPO, one of the state-of-the-art baselines, on the majority of math, reasoning, and coding benchmarks.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

As large language models (LLMs) scale up, accuracy improves, but the autoregressive (AR) nature of decoding increases latency since each token requires a serial forward pass. Speculative decoding addresses this by employing a fast drafter to propose multi-token drafts, which are then verified in parallel by the target model. However, many deployments still rely on AR drafters, where sequential passes limit wall-clock gains. We revisit the drafting stage and present DiffuSpec, a training-free drop-in framework that uses a pretrained diffusion language model (DLM) to produce multi-token drafts in a single forward pass, while remaining compatible with standard AR verifiers. Because DLM drafts are generated under bidirectional conditioning, parallel per-position candidates form a token lattice in which the locally highest-probability token at each position need not form a causal left-to-right path. Moreover, DLM drafting requires pre-specifying a draft length, inducing a speed-quality trade-off. To address these challenges, we introduce two practical components: (i) a causal-consistency path search (CPS) over this lattice that extracts a left-to-right path aligned with AR verification; and (ii) an adaptive draft-length (ADL) controller that adjusts next proposal size based on recent acceptance feedback and realized generated length. Across benchmarks, DiffuSpec yields up to 3x wall-clock speedup, establishing diffusion-based drafting as a robust alternative to autoregressive drafters for speculative decoding.

Masked Diffusion Language Models (DLMs) have recently emerged as a promising alternative to traditional Autoregressive Models (ARMs). DLMs employ transformer encoders with bidirectional attention, enabling parallel token generation while maintaining competitive performance. Although their efficiency and effectiveness have been extensively studied, the internal mechanisms that govern DLMs remain largely unexplored. In this work, we conduct an empirical analysis of DLM attention patterns, focusing on the attention sinking phenomenon, an effect previously observed in various transformer-based architectures. Our findings reveal that DLMs also exhibit attention sinks, but with distinct characteristics. First, unlike in ARMs, the sink positions in DLMs tend to shift throughout the generation process, displaying a dynamic behaviour. Second, while ARMs are highly sensitive to the removal of attention sinks, DLMs remain robust: masking sinks leads to only a minor degradation in performance. These results provide new insights into the inner workings of diffusion-based language models and highlight fundamental differences in how they allocate and utilize attention compared to autoregressive models.

Masked diffusion language models (MDLMs) have recently emerged as a promising alternative to autoregressive (AR) language models, offering properties such as parallel decoding, flexible generation orders, and the potential for fewer inference steps. Despite these advantages, decoding strategies and reinforcement learning (RL) algorithms tailored for MDLMs remain underexplored. A naive approach is to directly transfer techniques well-established for AR models to MDLMs. However, this raises an immediate question: Is such a naive transfer truly optimal? For example, 1) Block-wise and semi-AR decoding strategies are not employed during the training of MDLMs, so why do they outperform full diffusion-style decoding during inference? 2) Applying RL algorithms designed for AR models directly to MDLMs exhibits a training-inference inconsistency, since MDLM decoding are non-causal (parallel). This results in inconsistencies between the rollout trajectory and the optimization trajectory. To address these challenges, we propose EOS Early Rejection (EOSER) and Ascending Step-Size (ASS) decoding scheduler, which unlock the potential of MDLMs to perform full diffusion-style decoding, achieving competitive performance with fewer decoding steps. Additionally, we introduce Consistency Trajectory Group Relative Policy Optimization (CJ-GRPO) for taming MDLMs, which emphasizes the consistency between rollout trajectory and optimization trajectory, and reduces the optimization errors caused by skip-step optimization. We conduct extensive experiments on reasoning tasks, such as mathematical and planning benchmarks, using LLaDA-8B-Instruct. The results demonstrate that the proposed EOSER and ASS mechanisms, together with CJ-GRPO, hold significant promise for effectively and efficiently taming MDLMs. Code: https://github.com/yjyddq/EOSER-ASS-RL.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains. Code&pretrained checkpoints: https://github.com/apple/ml-fs-dfm

Modern LLM pre-training consumes vast amounts of compute and training data, making the scaling behavior, or scaling laws, of different models a key distinguishing factor. Discrete diffusion language models (DLMs) have been proposed as an alternative to autoregressive language models (ALMs). However, their scaling behavior has not yet been fully explored, with prior work suggesting that they require more data and compute to match the performance of ALMs. We study the scaling behavior of DLMs on different noise types by smoothly interpolating between masked and uniform diffusion while paying close attention to crucial hyperparameters such as batch size and learning rate. Our experiments reveal that the scaling behavior of DLMs strongly depends on the noise type and is considerably different from ALMs. While all noise types converge to similar loss values in compute-bound scaling, we find that uniform diffusion requires more parameters and less data for compute-efficient training compared to masked diffusion, making them a promising candidate in data-bound settings. We scale our uniform diffusion model up to 10B parameters trained for $10^{22}$ FLOPs, confirming the predicted scaling behavior and making it the largest publicly known uniform diffusion model to date.

Diffusion (Large) Language Models (dLLMs) now match the downstream performance of their autoregressive counterparts on many tasks, while holding the promise of being more efficient during inference. One particularly successful variant is masked discrete diffusion, in which a buffer filled with special mask tokens is progressively replaced with tokens sampled from the model's vocabulary. Efficiency can be gained by unmasking several tokens in parallel, but doing too many at once risks degrading the generation quality. Thus, one critical design aspect of dLLMs is the sampling procedure that selects, at each step of the diffusion process, which tokens to replace. Indeed, recent work has found that heuristic strategies such as confidence thresholding lead to both higher quality and token throughput compared to random unmasking. However, such heuristics have downsides: they require manual tuning, and we observe that their performance degrades with larger buffer sizes. In this work, we instead propose to train sampling procedures using reinforcement learning. Specifically, we formalize masked diffusion sampling as a Markov decision process in which the dLLM serves as the environment, and propose a lightweight policy architecture based on a single-layer transformer that maps dLLM token confidences to unmasking decisions. Our experiments show that these trained policies match the performance of state-of-the-art heuristics when combined with semi-autoregressive generation, while outperforming them in the full diffusion setting. We also examine the transferability of these policies, finding that they can generalize to new underlying dLLMs and longer sequence lengths. However, we also observe that their performance degrades when applied to out-of-domain data, and that fine-grained tuning of the accuracy-efficiency trade-off can be challenging with our approach.

Recently, diffusion models have garnered significant interest in the field of text processing due to their many potential advantages compared to conventional autoregressive models. In this work, we propose Diffusion-of-Thought (DoT), a novel approach that integrates diffusion models with Chain-of-Thought, a well-established technique for improving the reasoning ability of autoregressive language models. In contrast to autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT allows reasoning steps to diffuse over time through a diffusion language model and offers greater flexibility in trading-off computation for reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication, boolean logic, and grade school math problems, with a small diffusion model outperforming a much larger autoregressive model in both efficiency and accuracy. In addition to that, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning with diffusion language models.

We introduce the first watermark tailored for diffusion language models (DLMs), an emergent LLM paradigm able to generate tokens in arbitrary order, in contrast to standard autoregressive language models (ARLMs) which generate tokens sequentially. While there has been much work in ARLM watermarking, a key challenge when attempting to apply these schemes directly to the DLM setting is that they rely on previously generated tokens, which are not always available with DLM generation. In this work we address this challenge by: (i) applying the watermark in expectation over the context even when some context tokens are yet to be determined, and (ii) promoting tokens which increase the watermark strength when used as context for other tokens. This is accomplished while keeping the watermark detector unchanged. Our experimental evaluation demonstrates that the DLM watermark leads to a>99% true positive rate with minimal quality impact and achieves similar robustness to existing ARLM watermarks, enabling for the first time reliable DLM watermarking.

Social biases in text generation models severely compromise technical fairness and social inclusiveness. Existing studies mostly focus on debiasing at the word embedding level, ignoring dynamic biases in generated text, with limitations like low training efficiency and poor generalization. To address this, we propose Debias-Adapter, a bias mitigation method based on text diffusion models. Built on the Latent Diffusion Model (LDM) framework, it introduces a decoupled cross-attention mechanism and adds an adapter module to the Transformer-Encoder, optimizing only <5% of adapter parameters while freezing the pre-trained backbone to boost efficiency. Targeted data filtering and adaptation ensure input validity. Tested on the BBQ dataset, it outperforms baselines like Qwen3 and LD4LG, achieving a top accuracy of 73.7% and a maximum accuracy difference of 9.6% in non-ambiguous contexts, with significantly lower bias scores in both ambiguous and disambiguated contexts. This method exhibits strong debiasing effectiveness across multiple bias scenarios, supporting ethical optimization and fairness improvement of text generation models.

Masked diffusion models (MDMs) have shown promise in language modeling, yet their scalability and effectiveness in core language tasks, such as text generation and language understanding, remain underexplored. This paper establishes the first scaling law for MDMs, demonstrating a scaling rate comparable to autoregressive models (ARMs) and a relatively small compute gap. Motivated by their scalability, we train a family of MDMs with up to 1.1 billion (B) parameters to systematically evaluate their performance against ARMs of comparable or larger sizes. Fully leveraging the probabilistic formulation of MDMs, we propose a simple yet effective unsupervised classifier-free guidance that effectively exploits large-scale unpaired data, boosting performance for conditional inference. In language understanding, the 1.1B MDM outperforms the 1.1B TinyLlama model trained on the same data across four of eight zero-shot benchmarks. Notably, it achieves competitive math reasoning ability with the 7B Llama-2 model on the GSM8K dataset. In text generation, MDMs with 16 times more pre-training time offer a flexible trade-off against ARMs with the accelerated sampling technique KV-Cache: MDMs match ARMs in performance while being 1.4 times faster during sampling. Moreover, MDMs address challenging tasks for ARMs by effectively handling bidirectional reasoning and adapting to temporal shifts in data. Notably, a 1.1B MDM breaks the reverse curse encountered by much larger ARMs with significantly more data and computation, such as 13B Llama-2 and 175B GPT-3. Our code is available at https://github.com/ML-GSAI/SMDM.

Recently, diffusion models have emerged as a new paradigm for generative models. Despite the success in domains using continuous signals such as vision and audio, adapting diffusion models to natural language is under-explored due to the discrete nature of texts, especially for conditional generation. We tackle this challenge by proposing DiffuSeq: a diffusion model designed for sequence-to-sequence (Seq2Seq) text generation tasks. Upon extensive evaluation over a wide range of Seq2Seq tasks, we find DiffuSeq achieving comparable or even better performance than six established baselines, including a state-of-the-art model that is based on pre-trained language models. Apart from quality, an intriguing property of DiffuSeq is its high diversity during generation, which is desired in many Seq2Seq tasks. We further include a theoretical analysis revealing the connection between DiffuSeq and autoregressive/non-autoregressive models. Bringing together theoretical analysis and empirical evidence, we demonstrate the great potential of diffusion models in complex conditional language generation tasks. Code is available at \url{https://github.com/Shark-NLP/DiffuSeq}

Unified generation models aim to handle diverse tasks across modalities -- such as text generation, image generation, and vision-language reasoning -- within a single architecture and decoding paradigm. Autoregressive unified models suffer from slow inference due to sequential decoding, and non-autoregressive unified models suffer from weak generalization due to limited pretrained backbones. We introduce Muddit, a unified discrete diffusion transformer that enables fast and parallel generation across both text and image modalities. Unlike prior unified diffusion models trained from scratch, Muddit integrates strong visual priors from a pretrained text-to-image backbone with a lightweight text decoder, enabling flexible and high-quality multimodal generation under a unified architecture. Empirical results show that Muddit achieves competitive or superior performance compared to significantly larger autoregressive models in both quality and efficiency. The work highlights the potential of purely discrete diffusion, when equipped with strong visual priors, as a scalable and effective backbone for unified generation.

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to autoregressive (AR) LLMs for text generation, with the potential to decode multiple tokens in a single iteration. However, none of the existing open-source dLLMs have achieved superior inference speed over AR LLMs of similar size. This paper breaks this barrier based on a simple and effective strategy named discrete diffusion forcing (D2F). D2F equips dLLMs with two key capabilities: (1) block-wise autoregressive generation to enable KV cache utilization; (2) prediction of following tokens without requiring completion of prior blocks for inter-block parallel decoding. In this way, the vanilla dLLMs are refurbished into an AR-diffusion hybrid paradigm for efficient inference. D2F can be implemented with an asymmetric distillation process based on pre-trained dLLMs. We further propose a pipelined parallel decoding algorithm, which enables a trade-off between efficiency and efficacy. Empirically, D2F dLLMs achieve more than $\mathbf{2.5\times}$ inference speed than LLaMA3 and Qwen2.5 on GSM8K. Compared to vanilla dLLMs like LLaDA and Dream, the acceleration can be more than $\mathbf{50\times}$ while maintaining comparable output quality. The code is available at https://github.com/zhijie-group/Discrete-Diffusion-Forcing.

Discrete diffusion models are a new class of text generators that offer advantages such as bidirectional context use, parallelizable generation, and flexible prompting compared to autoregressive models. However, a critical limitation of discrete diffusion models is their inability to perform flexible-length or flexible-position text infilling without access to ground-truth positional data. We introduce \textbf{DDOT} (\textbf{D}iscrete \textbf{D}iffusion with \textbf{O}ptimal \textbf{T}ransport Position Coupling), the first discrete diffusion model to overcome this challenge. DDOT jointly denoises token values and token positions, employing a novel sample-level Optimal Transport (OT) coupling. This coupling preserves relative token ordering while dynamically adjusting the positions and length of infilled segments, a capability previously missing in text diffusion. Our method is orthogonal to existing discrete text diffusion methods and is compatible with various pretrained text denoisers. Extensive experiments on text infilling benchmarks such as One-Billion-Word and Yelp demonstrate that DDOT outperforms naive diffusion baselines. Furthermore, DDOT achieves performance on par with state-of-the-art non-autoregressive models and enables significant improvements in training efficiency and flexibility.

No abstract available

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $\tau$-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, $\tau$-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $\theta$-Trapezoidal method in KL divergence. Empirical evaluations on GSM8K-level math-reasoning, GPT-2-level text, and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints, with consistent performance gains across models ranging from 200M to 8B. Our code is available at https://github.com/yuchen-zhu-zyc/DiscreteFastSolver.

Multimodal generative models that can understand and generate across multiple modalities are dominated by autoregressive (AR) approaches, which process tokens sequentially from left to right, or top to bottom. These models jointly handle images, text, video, and audio for various tasks such as image captioning, question answering, and image generation. In this work, we explore discrete diffusion models as a unified generative formulation in the joint text and image domain, building upon their recent success in text generation. Discrete diffusion models offer several advantages over AR models, including improved control over quality versus diversity of generated samples, the ability to perform joint multimodal inpainting (across both text and image domains), and greater controllability in generation through guidance. Leveraging these benefits, we present the first Unified Multimodal Discrete Diffusion (UniDisc) model which is capable of jointly understanding and generating text and images for a variety of downstream tasks. We compare UniDisc to multimodal AR models, performing a scaling analysis and demonstrating that UniDisc outperforms them in terms of both performance and inference-time compute, enhanced controllability, editability, inpainting, and flexible trade-off between inference time and generation quality. Code and additional visualizations are available at https://unidisc.github.io.

Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current guidance methods aim to sample from a distribution with mass proportional to $p_0(x_0) p(\zeta|x_0)^\alpha$ but fail to achieve this in practice. We introduce a Sequential Monte Carlo algorithm that generates unbiasedly from this target distribution, utilising the learnt unconditional and guided process. We validate our approach on low-dimensional distributions, controlled images and text generations. For text generation, our method provides strong control while maintaining low perplexity compared to guidance-based approaches.

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by $25$-$75$\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around $6$-$8\times$ better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with $32\times$ fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to develop a family of reparameterized discrete diffusion models. The derived generic framework is highly flexible, offers a fresh perspective of the generation process in discrete diffusion models, and features more effective training and decoding techniques. We conduct extensive experiments to evaluate the text generation capability of our model, demonstrating significant improvements over existing diffusion models.

While diffusion models excel at conditional generating high-quality images, prior works in discrete diffusion models were not evaluated on conditional long-text generation. In this work, we address the limitations of prior discrete diffusion models for conditional long-text generation, particularly in long sequence-to-sequence tasks such as abstractive summarization. Despite fast decoding speeds compared to autoregressive methods, previous diffusion models failed on the abstractive summarization task due to the incompatibility between the backbone architectures and the random noising process. To overcome these challenges, we introduce a novel semantic-aware noising process that enables Transformer backbones to handle long sequences effectively. Additionally, we propose CrossMamba, an adaptation of the Mamba model to the encoder-decoder paradigm, which integrates seamlessly with the random absorbing noising process. Our approaches achieve state-of-the-art performance on three benchmark summarization datasets: Gigaword, CNN/DailyMail, and Arxiv, outperforming existing discrete diffusion models on ROUGE metrics as well as possessing much faster speed in inference compared to autoregressive models.

Recently, continuous diffusion models (CDM) have been introduced into non-autoregressive (NAR) text-to-text generation. However, the discrete nature of text increases the difficulty of CDM to generate coherent and fluent texts, and also causes the incompatibility problem between CDM and advanced NLP techniques, especially the popular pre-trained language models (PLMs).To solve it, we propose Diffusion-NAT, which introduces discrete diffusion models (DDM) into NAR text-to-text generation and integrates BART to improve the performance.By revising the decoding process of BART and the typical settings of DDM, we unify the inference process of BART and the denoising process of DDM into the same NAR masked tokens recovering task.In this way, DDM can rely on BART to perform denoising, which can benefit from both the rich pre-learned knowledge of BART and the iterative refining paradigm of DDM.Besides, we also propose the iterative self-prompting strategy to further improve the generation quality.Experimental results on 7 datasets show that our approach can outperform competitive NAR methods, and even surpass autoregressive methods.Our code and data are released at https://github.com/RUCAIBox/DiffusionNAT.

No abstract available

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices. We begin by deriving an upper bound on the KL divergence of the forward process, introducing a surrogate initialization distribution to address the challenge posed by the absorbing stationary distribution, which is a singleton and causes the KL divergence to be ill-defined. We then establish the first convergence guarantees for both the $\tau$-leaping and uniformization samplers under absorbing rate matrices, demonstrating improved rates over their counterparts using uniform rate matrices. Furthermore, under suitable assumptions, we provide convergence guarantees without early stopping. Our analysis introduces several new technical tools to address challenges unique to absorbing rate matrices. These include a Jensen-type argument for bounding forward process convergence, novel techniques for bounding absorbing score functions, and a non-divergent upper bound on the score near initialization that removes the need of early-stopping.

Diffusion models have seen notable success in continuous domains, leading to the development of discrete diffusion models (DDMs) for discrete variables. Despite recent advances, DDMs face the challenge of slow sampling speeds. While parallel sampling methods like $\tau$-leaping accelerate this process, they introduce $\textit{Compounding Decoding Error}$ (CDE), where discrepancies arise between the true distribution and the approximation from parallel token generation, leading to degraded sample quality. In this work, we present $\textit{Jump Your Steps}$ (JYS), a novel approach that optimizes the allocation of discrete sampling timesteps by minimizing CDE without extra computational cost. More precisely, we derive a practical upper bound on CDE and propose an efficient algorithm for searching for the optimal sampling schedule. Extensive experiments across image, music, and text generation show that JYS significantly improves sampling quality, establishing it as a versatile framework for enhancing DDM performance for fast sampling.

Masked diffusion models (MDM) are powerful generative models for discrete data that generate samples by progressively unmasking tokens in a sequence. Each token can take one of two states: masked or unmasked. We observe that token sequences often remain unchanged between consecutive sampling steps; consequently, the model repeatedly processes identical inputs, leading to redundant computation. To address this inefficiency, we propose the Partial masking scheme (Prime), which augments MDM by allowing tokens to take intermediate states interpolated between the masked and unmasked states. This design enables the model to make predictions based on partially observed token information, and facilitates a fine-grained denoising process. We derive a variational training objective and introduce a simple architectural design to accommodate intermediate-state inputs. Our method demonstrates superior performance across a diverse set of generative modeling tasks. On text data, it achieves a perplexity of 15.36 on OpenWebText, outperforming previous MDM (21.52), autoregressive models (17.54), and their hybrid variants (17.58), without relying on an autoregressive formulation. On image data, it attains competitive FID scores of 3.26 on CIFAR-10 and 6.98 on ImageNet-32, comparable to leading continuous generative models.

Generative modeling of discrete data underlies important applications spanning text-based agents like ChatGPT to the design of the very building blocks of life in protein sequences. However, application domains need to exert control over the generated data by steering the generative process - typically via RLHF - to satisfy a specified property, reward, or affinity metric. In this paper, we study the problem of steering Masked Diffusion Models (MDMs), a recent class of discrete diffusion models that offer a compelling alternative to traditional autoregressive models. We introduce Discrete Denoising Posterior Prediction (DDPP), a novel framework that casts the task of steering pre-trained MDMs as a problem of probabilistic inference by learning to sample from a target Bayesian posterior. Our DDPP framework leads to a family of three novel objectives that are all simulation-free, and thus scalable while applying to general non-differentiable reward functions. Empirically, we instantiate DDPP by steering MDMs to perform class-conditional pixel-level image modeling, RLHF-based alignment of MDMs using text-based rewards, and finetuning protein language models to generate more diverse secondary structures and shorter proteins. We substantiate our designs via wet-lab validation, where we observe transient expression of reward-optimized protein sequences.

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot vectors and cannot be propagated across steps, forcing subsequent steps to operate with limited information. To mitigate this problem, we introduce Loopholing, a novel and simple mechanism that preserves this information via a deterministic latent pathway, leading to Loopholing Discrete Diffusion Models (LDDMs). Trained efficiently with a self-conditioning strategy that avoids unrolling the full denoising trajectory, LDDMs achieve substantial gains-reducing generative perplexity by up to 61% over prior baselines, thereby closing (and in some cases surpassing) the gap with autoregressive models, and producing more coherent text. Applied to reasoning tasks, LDDMs also improve performance on arithmetic benchmarks such as Countdown and Game of 24. These results also indicate that loopholing mitigates idle steps and oscillations, providing a general and effective path toward high-quality non-autoregressive text generation.

Diffusion models have emerged as a promising approach for text generation, with recent works falling into two main categories: discrete and continuous diffusion models. Discrete diffusion models apply token corruption independently using categorical distributions, allowing for different diffusion progress across tokens but lacking fine-grained control. Continuous diffusion models map tokens to continuous spaces and apply fine-grained noise, but the diffusion progress is uniform across tokens, limiting their ability to capture semantic nuances. To address these limitations, we propose \textbf{\underline{N}}on-simultan\textbf{\underline{e}}ous C\textbf{\underline{o}}ntinuous \textbf{\underline{Diff}}usion Models (NeoDiff), a novel diffusion model that integrates the strengths of both discrete and continuous approaches. NeoDiff introduces a Poisson diffusion process for the forward process, enabling a flexible and fine-grained noising paradigm, and employs a time predictor for the reverse process to adaptively modulate the denoising progress based on token semantics. Furthermore, NeoDiff utilizes an optimized schedule for inference to ensure more precise noise control and improved performance. Our approach unifies the theories of discrete and continuous diffusion models, offering a more principled and effective framework for text generation. Experimental results on several text generation tasks demonstrate NeoDiff's superior performance compared to baselines of non-autoregressive continuous and discrete diffusion models, iterative-based methods and autoregressive diffusion-based methods. These results highlight NeoDiff's potential as a powerful tool for generating high-quality text and advancing the field of diffusion-based text generation.

While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free guidance, making it well-suited for posterior sampling. Existing approaches to posterior sampling using discrete diffusion face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS), built on two key innovations: quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. APS achieves state-of-the-art performance among discrete diffusion samplers on both linear and nonlinear inverse problems across the standard image benchmarks. We demonstrate the generality of APS through training-free stylization and text-guided editing. We further apply APS to a large-scale diffusion language model, showing consistent improvement in question answering.

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at \href{https://github.com/feiyangfu/LSD}{https://github.com/feiyangfu/LSD}.

Masked Discrete Diffusion Models (MDMs) have achieved strong performance across a wide range of multimodal tasks, including image understanding, generation, and editing. However, their inference speed remains suboptimal due to the need to repeatedly process redundant masked tokens at every sampling step. In this work, we propose Sparse-LaViDa, a novel modeling framework that dynamically truncates unnecessary masked tokens at each inference step to accelerate MDM sampling. To preserve generation quality, we introduce specialized register tokens that serve as compact representations for the truncated tokens. Furthermore, to ensure consistency between training and inference, we design a specialized attention mask that faithfully matches the truncated sampling procedure during training. Built upon the state-of-the-art unified MDM LaViDa-O, Sparse-LaViDa achieves up to a 2x speedup across diverse tasks including text-to-image generation, image editing, and mathematical reasoning, while maintaining generation quality.

Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively unmasking multiple dimensions from an all-masked input, but their performance can degrade when using few denoising steps due to limited modeling of inter-dimensional dependencies. In this paper, we propose Variational Autoencoding Discrete Diffusion (VADD), a novel framework that enhances discrete diffusion with latent variable modeling to implicitly capture correlations among dimensions. By introducing an auxiliary recognition model, VADD enables stable training via variational lower bounds maximization and amortized inference over the training set. Our approach retains the efficiency of traditional MDMs while significantly improving sample quality, especially when the number of denoising steps is small. Empirical results on 2D toy data, pixel-level image generation, and text generation demonstrate that VADD consistently outperforms MDM baselines.

Test-time scaling through reward-guided generation remains largely unexplored for discrete diffusion models despite its potential as a promising alternative. In this work, we introduce Iterative Reward-Guided Refinement (IterRef), a novel test-time scaling method tailored to discrete diffusion that leverages reward- guided noising-denoising transitions to progressively refine misaligned intermediate states. We formalize this process within a Multiple-Try Metropolis (MTM) framework, proving convergence to the reward-aligned distribution. Unlike prior methods that assume the current state is already aligned with the reward distribution and only guide the subsequent transition, our approach explicitly refines each state in situ, progressively steering it toward the optimal intermediate distribution. Across both text and image domains, we evaluate IterRef on diverse discrete diffusion models and observe consistent improvements in reward-guided generation quality. In particular, IterRef achieves striking gains under low compute budgets, far surpassing prior state-of-the-art baselines.

Recent advances in generative medical models are constrained by modality-specific scenarios that hinder the integration of complementary evidence from imaging, pathology, and clinical notes. This fragmentation limits their evolution into foundation models that can learn and reason across the full spectrum of biomedical data. We propose MeDiM, the first medical discrete diffusion model that learns shared distributions across modalities without modality-specific components. MeDiM unifies multiple generative tasks: translating between images and text, and jointly producing image-report pairs across domains in response to prompts. Built on a discrete diffusion framework, MeDiM bridges vision and language representations through a shared probabilistic space. To enable unified and flexible medical generation, we employ a multimodal large language model (MLLM) as the diffusion backbone, leveraging its prior knowledge and cross-modal reasoning. Two key designs are introduced: (1) removing the causal attention mask for bidirectional context, and (2) injecting continuous timestep embeddings for diffusion awareness. Experiments demonstrate high-fidelity medical generation (FID 16.60 on MIMIC-CXR and FID 24.19 on PathGen) and accurate report generation (METEOR 0.2650 and 0.2580). Jointly generated image-report pairs further enhance downstream performance (plus6.43 percent BLEU-1, plus18.57 percent BLEU-2, plus31.58 percent BLEU-3, plus4.80 percent METEOR), showing that MeDiM supports coherent and clinically grounded multimodal outputs.

Current autoregressive language models (ARMs) achieve high accuracy but require long token sequences, making them costly. Discrete diffusion language models (DDLMs) enable parallel and flexible generation within a fixed number of steps and have recently emerged for their strong performance in complex reasoning and long-term planning tasks. We present a study exploring hybrid architectures that couple DDLMs with ARMs to assess whether their collaboration can yield complementary benefits. We first examine collaboration in text space, where one model plans the reasoning process and another executes the final answer based on that plan. We then extend this setup to latent-space communication, introducing a learned projector that maps DDLM latents into the ARM's embedding space, potentially bypassing some of the text-generation limitations of diffusion models. We find that shifting DDLM -->ARM communication from text space to latent space yields significant accuracy gains, for example increasing from 27.0% to 54.0% on DART-5 and from 0.0% to 14.0% on AIME24. We also find that combining a DDLM planner with an ARM executor can provide substantial computational savings with little to no impact on accuracy. For example, the latent-space pipeline, using 64 tokens for planning and roughly 5 for execution, surpasses Qwen3.1-7B on DART-5 and AIME, despite Qwen using 44 times more tokens. Overall, our study offers new insights into reasoning with DDLMs and highlights their potential in hybrid architectures.

Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected denoiser output under the forward corruption distribution recovers the true posterior, and that a simple Monte Carlo estimator converges to this posterior at rate O(1/sqrt(K)) with finite-sample concentration bounds. Building on this insight, we introduce an inference-time ensemble that runs K independent denoising passes and aggregates both posterior means and variances without any extra training. On WikiText-2, our MC-marginal sampler recovers the analytic lambda-DCE zero-shot perplexity (approximately 39) to within a few points at K=128, and its per-token variance shows a strong rank correlation with reconstruction error (Spearman rho = 0.996). This cost-proportional procedure yields calibrated uncertainty estimates and a direct trade-off between compute and posterior fidelity in discrete diffusion LMs.

In the domains of image and audio, diffusion models have shown impressive performance. However, their application to discrete data types, such as language, has often been suboptimal compared to autoregressive generative models. This paper tackles the challenge of improving discrete diffusion models by introducing a structured forward process that leverages the inherent information hierarchy in discrete categories, such as words in text. Our approach biases the generative process to produce certain categories before others, resulting in a notable improvement in log-likelihood scores on the text8 dataset. This work paves the way for more advances in discrete diffusion models with potentially significant enhancements in performance.

Although auto-regressive models excel in natural language processing, they often struggle to generate diverse text and provide limited controllability. Non-auto-regressive methods could be an alternative but often produce degenerate outputs and exhibit shortcomings in conditional generation. To address these challenges, we propose Diffusion-EAGS, a novel framework that integrates conditional masked language models into diffusion language models through the theoretical lens of a conditional Markov Random Field. In doing so, we propose entropy-adaptive Gibbs sampling and entropy-based noise scheduling to counterbalance each model's shortcomings. Experimental results show that Diffusion-EAGS outperforms baselines and achieves the best quality-diversity tradeoff, demonstrating its effectiveness in non-autoregressive text generation.

The application of deep generative models for molecular discovery has witnessed a significant surge in recent years. Currently, the field of molecular generation and molecular optimization is predominantly governed by autoregressive models regardless of how molecular data is represented. However, an emerging paradigm in the generation domain is diffusion models, which treat data non-autoregressively and have achieved significant breakthroughs in areas such as image generation. The potential and capability of diffusion models in molecular generation and optimization tasks remain largely unexplored. In order to investigate the potential applicability of diffusion models in the domain of molecular exploration, we proposed DiffSeqMol, a molecular sequence generation model, underpinned by diffusion process. DiffSeqMol distinguishes itself from traditional autoregressive methods by its capacity to draw samples from random noise and direct generating the entire molecule. Through experiment evaluations, we demonstrated that DiffSeqMol can achieve, even surpass, the performance of established state-of-the-art models on unconditional generation tasks and molecular optimization tasks. Taken together, our results show that DiffSeqMol can be considered a promising molecular generation method. It opens new pathways to traverse the expansive chemical space and to discover novel molecules.

Recent advances in large language models (LLMs) have attracted significant interest in extending their capabilities to multimodal scenarios, particularly for speech-to-speech conversational systems. However, existing multimodal models handling interleaved audio and text rely on autoregressive (AR) methods, overlooking that text depends on target-target relations whereas audio depends mainly on source-target relations. In this work, we propose Text-to-Talk (TtT), a unified audio-text framework that integrates AR text generation with non-autoregressive (NAR) audio diffusion in a single Transformer. By leveraging the any-order AR property of absorbing discrete diffusion, our approach provides a unified training objective for text and audio. To support this hybrid generation paradigm, we design a modality-aware attention mechanism that enforces causal decoding for text while allowing bidirectional modeling within audio spans, and further introduce three training strategies that reduce train-test discrepancies. During inference, TtT employs block-wise diffusion to synthesize audio in parallel while flexibly handling variable-length outputs. Comprehensive experiments on Audio-QA, ASR, AAC and speech-to-speech benchmarks show that TtT consistently surpasses strong AR and NAR baselines, with additional ablation and training-strategy analyses confirming the contribution of each component. We will open-source our models, data and code to facilitate future research in this direction.

Diffusion language models (dLMs) have emerged as a promising paradigm that enables parallel, non-autoregressive generation, but their learning efficiency lags behind that of autoregressive (AR) language models when trained from scratch. To this end, we study AR-to-dLM conversion to transform pretrained AR models into efficient dLMs that excel in speed while preserving AR models'task accuracy. We achieve this by identifying limitations in the attention patterns and objectives of existing AR-to-dLM methods and then proposing principles and methodologies for more effective AR-to-dLM conversion. Specifically, we first systematically compare different attention patterns and find that maintaining pretrained AR weight distributions is critical for effective AR-to-dLM conversion. As such, we introduce a continuous pretraining scheme with a block-wise attention pattern, which remains causal across blocks while enabling bidirectional modeling within each block. We find that this approach can better preserve pretrained AR models'weight distributions than fully bidirectional modeling, in addition to its known benefit of enabling KV caching, and leads to a win-win in accuracy and efficiency. Second, to mitigate the training-test gap in mask token distributions (uniform vs. highly left-to-right), we propose a position-dependent token masking strategy that assigns higher masking probabilities to later tokens during training to better mimic test-time behavior. Leveraging this framework, we conduct extensive studies of dLMs'attention patterns, training dynamics, and other design choices, providing actionable insights into scalable AR-to-dLM conversion. These studies lead to the Efficient-DLM family, which outperforms state-of-the-art AR models and dLMs, e.g., our Efficient-DLM 8B achieves +5.4%/+2.7% higher accuracy with 4.5x/2.7x higher throughput compared to Dream 7B and Qwen3 4B, respectively.

Controlling the behavior of language models (LMs) without re-training is a major open problem in natural language generation. While recent works have demonstrated successes on controlling simple sentence attributes (e.g., sentiment), there has been little progress on complex, fine-grained controls (e.g., syntactic structure). To address this challenge, we develop a new non-autoregressive language model based on continuous diffusions that we call Diffusion-LM. Building upon the recent successes of diffusion models in continuous domains, Diffusion-LM iteratively denoises a sequence of Gaussian vectors into word vectors, yielding a sequence of intermediate latent variables. The continuous, hierarchical nature of these intermediate variables enables a simple gradient-based algorithm to perform complex, controllable generation tasks. We demonstrate successful control of Diffusion-LM for six challenging fine-grained control tasks, significantly outperforming prior work.

LLMs have become the mainstream approaches to code generation. Existing LLMs mainly employ autoregressive generation, i.e. generating code token-by-token from left to right. However, the underlying autoregressive generation has two limitations in code generation. First, autoregressive LLMs only generate a token at each step, showing low efficiency in practice. Second, programming is a non-sequential process involving back-and-forth editing, while autoregressive LLMs only employ the left-to-right generation order. These two intrinsic limitations hinder the further development of LLMs in code generation. Recently, diffusion LLMs have emerged as a promising alternative. Diffusion LLMs address the above limitations with two advances, including multi-token prediction (i.e. generating multiple tokens at each step) and flexible generation order (i.e. flexibly determining which positions to generate tokens). However, there is no systematic study exploring diffusion LLMs in code generation. To bridge the knowledge gap, we present the first empirical study of diffusion LLMs for code generation. Our study involves 9 representative diffusion LLMs and conduct experiments on 4 widely used benchmarks. Based on the results, we summarize the following findings. (1) Existing diffusion LLMs are competitive with autoregressive LLMs with similar sizes. (2) Diffusion LLMs have a stronger length extrapolation ability than autoregressive LLMs and perform better in long code understanding. (3) We explore factors impacting the effectiveness and efficiency of diffusion LLMs, and provide practical guidance. (4) We discuss several promising further directions to improve diffusion LLMs on code generation. We open-source all source code, data, and results to facilitate the following research. The code is publicly available at https://github.com/zhangyitonggg/dllm4code.

Diffusion-based large language models (Diffusion LLMs) have shown promise for non-autoregressive text generation with parallel decoding capabilities. However, the practical inference speed of open-sourced Diffusion LLMs often lags behind autoregressive models due to the lack of Key-Value (KV) Cache and quality degradation when decoding multiple tokens simultaneously. To bridge this gap, we introduce a novel block-wise approximate KV Cache mechanism tailored for bidirectional diffusion models, enabling cache reuse with negligible performance drop. Additionally, we identify the root cause of generation quality degradation in parallel decoding as the disruption of token dependencies under the conditional independence assumption. To address this, we propose a confidence-aware parallel decoding strategy that selectively decodes tokens exceeding a confidence threshold, mitigating dependency violations and maintaining generation quality. Experimental results on LLaDA and Dream models across multiple LLM benchmarks demonstrate up to \textbf{27.6$\times$ throughput} improvement with minimal accuracy loss, closing the performance gap with autoregressive models and paving the way for practical deployment of Diffusion LLMs.

This study proposes an image captioning method designed to incorporate user-specific explanatory intentions into the generated text, as signaled by the user’s trace on the image. We extract areas of interest from dense sections of the trace, determine the order of explanations by tracking changes in the pen-tip coordinates, and assess the degree of interest in each area by analyzing the time spent on them. Additionally, a diffusion language model is utilized to generate sentences in a non-autoregressive manner, allowing control over sentence length based on the temporal data of the trace. In the actual caption generation task, the proposed method achieved higher string similarity than conventional methods, including autoregressive models, and successfully captured user intent from the trace and faithfully reflected it in the generated text.

Discrete diffusion models offer a flexible, controllable approach to structured sequence generation, yet they still lag behind causal language models in expressive power. A key limitation lies in their reliance on the Markovian assumption, which restricts each step to condition only on the current state, leading to potential uncorrectable error accumulation. In this paper, we introduce CaDDi (Causal Discrete Diffusion Model), a discrete diffusion model that conditions on the entire generative trajectory, thereby lifting the Markov constraint and allowing the model to revisit and improve past states. By unifying sequential (causal) and temporal (diffusion) reasoning in a single non-Markovian transformer, CaDDi also treats standard causal language models as a special case and permits the direct reuse of pretrained LLM weights with no architectural changes. Empirically, CaDDi outperforms state-of-the-art discrete diffusion baselines on natural-language benchmarks, substantially narrowing the remaining gap to large autoregressive transformers.

Existing radiology report generation (RRG) studies mostly adopt autoregressive (AR) approaches to produce textual descriptions token-by-token for specific clinical radiographs, where they are susceptible to error propagation problems if irrelevant contents are half-way generated, leading to potential ill-presenting of precise diagnoses, especially when there exist complicated abnormalities in radiographs. Although the non-AR paradigm, e.g., diffusion model, provides an alternative solution to tackle the problem from AR by generating all contents in parallel, the mechanism of using Gaussian noise in existing diffusion models still has significant room to improve when such models are used in particular circumstances, i.e., providing proper guidance in controlling noises in the diffusive process to ensure precise report generation. In this paper, we propose to conduct RRG with diffusion networks by controlling the noise with task-specific features, which leverages irrelevant visual and textual information as noise rather than the stochastic Gaussian noise, and allows the diffusion networks to filter particular information through iterative denoising, thus performing a precise and controlled report generation process. Experiments on IU X-Ray and MIMIC-CXR demonstrate the superiority of our approach compared to strong baselines and state-of-the-art solutions. Human evaluation and noise type analysis show that comprehensive noise control greatly helps diffusion networks to refine the generation of global and local report contents.

Recent large language models (LLMs) have demonstrated strong reasoning capabilities that benefits from online reinforcement learning (RL). These capabilities have primarily been demonstrated within the left-to-right autoregressive (AR) generation paradigm. In contrast, non-autoregressive paradigms based on diffusion generate text in a coarse-to-fine manner. Although recent diffusion-based large language models (dLLMs) have achieved competitive language modeling performance compared to their AR counterparts, it remains unclear if dLLMs can also leverage recent advances in LLM reasoning. To this end, we propose d1, a framework to adapt pre-trained masked dLLMs into reasoning models via a combination of supervised finetuning (SFT) and RL. Specifically, we develop and extend techniques to improve reasoning in pretrained dLLMs: (a) we utilize a masked SFT technique to distill knowledge and instill self-improvement behavior directly from existing datasets, and (b) we introduce a novel critic-free, policy-gradient based RL algorithm called diffu-GRPO, the first integration of policy gradient methods to masked dLLMs. Through empirical studies, we investigate the performance of different post-training recipes on multiple mathematical and planning benchmarks. We find that d1 yields the best performance and significantly improves performance of a state-of-the-art dLLM. Our code is released at https://dllm-reasoning.github.io/.

Diffusion language models (Diffusion-LMs) introduce an explicit temporal dimension into text generation, yet how this structure can be leveraged to control generation diversity for exploring multiple valid semantic or reasoning paths remains underexplored. In this paper, we show that Diffusion-LMs, like diffusion models in image generation, exhibit a temporal division of labor: early denoising steps largely determine the global semantic structure, while later steps focus on local lexical refinement. Building on this insight, we propose Time-Annealed Perturbation Sampling (TAPS), a training-free inference strategy that encourages semantic branching early in the diffusion process while progressively reducing perturbations to preserve fluency and instruction adherence. TAPS is compatible with both non-autoregressive and semi-autoregressive Diffusion backbones, demonstrated on LLaDA and TraDo in our paper, and consistently improves output diversity across creative writing and reasoning benchmarks without compromising generation quality.

No abstract available

Diffusion language models (dLLMs) offer a promising, non-autoregressive paradigm for text generation, yet training them for complex reasoning remains a key challenge. Current reinforcement learning approaches often rely on sparse, outcome-based rewards, which can reinforce flawed reasoning paths that lead to coincidentally correct answers. We argue that this stems from a fundamental mismatch with the natural structure of reasoning. We first propose a theoretical framework that formalizes complex problem solving as a hierarchical selection process, where an intractable global constraint is decomposed into a series of simpler, localized logical steps. This framework provides a principled foundation for algorithm design, including theoretical insights into the identifiability of this latent reasoning structure. Motivated by this theory, we identify unstructured refinement -- a failure mode where a model's iterative steps do not contribute meaningfully to the solution -- as a core deficiency in existing methods. We then introduce Step-Aware Policy Optimization (SAPO), a novel RL algorithm that aligns the dLLM's denoising process with the latent reasoning hierarchy. By using a process-based reward function that encourages incremental progress, SAPO guides the model to learn structured, coherent reasoning paths. Our empirical results show that this principled approach significantly improves performance on challenging reasoning benchmarks and enhances the interpretability of the generation process.

Diffusion language models have recently emerged as a competitive alternative to autoregressive language models. Beyond next-token generation, they are more efficient and flexible by enabling parallel and any-order token generation. However, despite empirical successes, their computational power and fundamental limitations remain poorly understood. In this paper, we formally study whether non-autoregressive generation in Masked Diffusion Models (MDM) enables solving problems beyond the reach of Auto-Regressive Models (ARM). Our results show that MDM with sufficiently large context length is computationally universal with decoding steps matching the optimal parallel time complexity in PRAM. However, when controlling for other factors, MDM's flexibility to generate in any-order does not expand what ARM can already solve. To address this, we propose a new form of generation called any-process generation, which extends MDM with capabilities to remask, insert and delete tokens, allowing self-correction, length-variable editing, and adaptive parallelism. Theoretically and empirically, we demonstrate these capabilities enable scalability to significantly harder reasoning problems that are otherwise intractable for ARM and vanilla MDM. Additionally, they prove essential for generation tasks where objects naturally evolve through non-sequential processes, crucial for extending current LLMs beyond natural language to domains such as coding and science.

Vision-language-action (VLA) models aim to understand natural language instructions and visual observations and to execute corresponding actions as an embodied agent. Recent work integrates future images into the understanding-acting loop, yielding unified VLAs that jointly understand, generate, and act -- reading text and images and producing future images and actions. However, these models either rely on external experts for modality unification or treat image generation and action prediction as separate processes, limiting the benefits of direct synergy between these tasks. Our core philosophy is to optimize generation and action jointly through a synchronous denoising process, where the iterative refinement enables actions to evolve from initialization, under constant and sufficient visual guidance. We ground this philosophy in our proposed Unified Diffusion VLA and Joint Discrete Denoising Diffusion Process (JD3P), which is a joint diffusion process that integrates multiple modalities into a single denoising trajectory to serve as the key mechanism enabling understanding, generation, and acting to be intrinsically synergistic. Our model and theory are built on a unified tokenized space of all modalities and a hybrid attention mechanism. We further propose a two-stage training pipeline and several inference-time techniques that optimize performance and efficiency. Our approach achieves state-of-the-art performance on benchmarks such as CALVIN, LIBERO, and SimplerEnv with 4$\times$ faster inference than autoregressive methods, and we demonstrate its effectiveness through in-depth analysis and real-world evaluations. Our project page is available at https://irpn-eai.github.io/UD-VLA.github.io/.

In recent years, diffusion based methods have emerged as a powerful paradigm for generative modeling. Although discrete diffusion for natural language processing has been explored to a lesser extent, it shows promise for tasks requiring iterative denoising of token based data. In standard approaches to text generation, transformers dominate, but their reliance on self attention often incurs high computational costs. This paper introduces a fully diffusion driven discrete text generation model built without any transformer or large convolution modules. Instead, the model integrates structured state space dynamics in the time domain with a novel Complex Fourier Multi Layer Perceptron module that operates in the frequency domain. The forward noising process randomly samples the vocabulary to replace tokens with a controlled probability, while the learned reverse model systematically reverts corrupted sequences toward their original states. By composing local state space updates with global Fourier based mixing, the approach effectively captures both short and long range dependencies.

No abstract available

In this work, we propose Dimple, the first Discrete Diffusion Multimodal Large Language Model (DMLLM). We observe that training with a purely discrete diffusion approach leads to significant training instability, suboptimal performance, and severe length bias issues. To address these challenges, we design a novel training paradigm that combines an initial autoregressive phase with a subsequent diffusion phase. This approach yields the Dimple-7B model, trained on the same dataset and using a similar training pipeline as LLaVA-NEXT. Dimple-7B ultimately surpasses LLaVA-NEXT in performance by 3.9%, demonstrating that DMLLM can achieve performance comparable to that of autoregressive models. To improve inference efficiency, we propose a decoding strategy termed confident decoding, which dynamically adjusts the number of tokens generated at each step, significantly reducing the number of generation iterations. In autoregressive models, the number of forward iterations during generation equals the response length. With confident decoding, however, the number of iterations needed by Dimple is even only $\frac{\text{response length}}{3}$. We also re-implement the prefilling technique in autoregressive models and demonstrate that it does not significantly impact performance on most benchmark evaluations, while offering a speedup of 1.5x to 7x. Additionally, we explore Dimple's capability to precisely control its response using structure priors. These priors enable structured responses in a manner distinct from instruction-based or chain-of-thought prompting, and allow fine-grained control over response format and length, which is difficult to achieve in autoregressive models. Overall, this work validates the feasibility and advantages of DMLLM and enhances its inference efficiency and controllability. Code and models are available at https://github.com/yu-rp/Dimple.

While most autoregressive LLMs are constrained to one-by-one decoding, diffusion LLMs (dLLMs) have attracted growing interest for their potential to dramatically accelerate inference through parallel decoding. Despite this promise, the conditional independence assumption in dLLMs causes parallel decoding to ignore token dependencies, inevitably degrading generation quality when these dependencies are strong. However, existing works largely overlook these inherent challenges, and evaluations on standard benchmarks (e.g., math and coding) are not sufficient to capture the quality degradation caused by parallel decoding. To address this gap, we first provide an information-theoretic analysis of parallel decoding. We then conduct case studies on analytically tractable synthetic list operations from both data distribution and decoding strategy perspectives, offering quantitative insights that highlight the fundamental limitations of parallel decoding. Building on these insights, we propose ParallelBench, the first benchmark specifically designed for dLLMs, featuring realistic tasks that are trivial for humans and autoregressive LLMs yet exceptionally challenging for dLLMs under parallel decoding. Using ParallelBench, we systematically analyze both dLLMs and autoregressive LLMs, revealing that: (i) dLLMs under parallel decoding can suffer dramatic quality degradation in real-world scenarios, and (ii) current parallel decoding strategies struggle to adapt their degree of parallelism based on task difficulty, thus failing to achieve meaningful speedup without compromising quality. Our findings underscore the pressing need for innovative decoding methods that can overcome the current speed-quality trade-off. We release our benchmark to help accelerate the development of truly efficient dLLMs.

The generation speed of LLMs are bottlenecked by autoregressive decoding, where tokens are predicted sequentially one by one. Alternatively, diffusion large language models (dLLMs) theoretically allow for parallel token generation, but in practice struggle to achieve the speed of autoregressive models without significantly sacrificing quality. We therefore introduce adaptive parallel decoding (APD), a novel method that dynamically adjusts the number of tokens sampled in parallel. We achieve this by defining a multiplicative mixture between the dLLM marginal probabilities and the joint probability of sequences under a small auxiliary autoregressive model. This inverts the standard setup of speculative decoding, where the goal is to sample from a large autoregressive verifier by drafting from a smaller model. We further optimize APD by enabling KV caching and limiting the size of the masked input. Altogether, our method puts forward three tunable parameters to flexibly tradeoff throughput and quality. We show that APD provides markedly higher throughput with minimal quality degradations on downstream benchmarks.

Diffusion Large Language Models (DLLMs) have emerged as a new paradigm of language modeling beyond autoregressive next-token prediction. Taking advantage of their inherent modeling foundations, DLLMs have the great potential of efficient inference with parallel decoding algorithms, which enable multi-token prediction. However, the high generation quality often requires the number of decoding steps equal to the sequence length, which performs a one-token-per-step decoding, and existing parallel decoding algorithms, which yield suboptimal decoding paths, bring inference speedup at the cost of non-negligible performance degradation. To overcome this challenge, we introduce Free Draft-and-Verification (FreeDave), a novel fast decoding algorithm tailored for DLLMs that achieves lossless parallel decoding without any model modification or extra modules. Specifically, we propose an algorithm of parallel-decoded candidate generation and verification, which is theoretically guaranteed to use the fewest model forward calls to reproduce the same sequence generated by one-token-per-step decoding. By extensive evaluations on math reasoning and code generation benchmarks across different DLLMs, FreeDave is proven to accelerate the inference up to $2.83\times$ without performance degradation.

Diffusion large language models (dLLMs) generate text through iterative denoising steps, achieving parallel decoding by denoising only high-confidence positions at each step. However, existing approaches often repetitively remask tokens due to initially low confidence scores, leading to redundant iterations and limiting overall acceleration. Through the analysis of dLLM decoding traces, we observe that the model often determines the final prediction for a token several steps before the decoding step. To leverage this historical information and avoid redundant steps, we introduce the concept of Trace Credit, which quantifies each token's convergence potential by accumulating historical logits. Furthermore, we propose CreditDecoding, a training-free parallel decoding algorithm that accelerates the confidence convergence of correct but underconfident tokens by fusing current logits with Trace Credit. This process significantly reduces redundant iterations and enhances decoding robustness. On eight benchmarks, CreditDecoding achieves a 5.48 times speedup and a 0.48 performance improvement over LLaDA-8B-Instruct, and a 4.11 times speedup with a 0.15 performance improvement over LLaDA-MoE-Instruct. Importantly, CreditDecoding scales effectively to long sequences and is orthogonal to mainstream inference optimizations, making it a readily integrable and versatile solution.

No abstract available

Diffusion large language models (dLLMs) have recently drawn considerable attention within the research community as a promising alternative to autoregressive generation, offering parallel token prediction and lower inference latency. Yet, their parallel decoding potential remains largely underexplored, as existing open-source models still require nearly token-length decoding steps to ensure performance. To address this, we introduce dParallel, a simple and effective method that unlocks the inherent parallelism of dLLMs for fast sampling. We identify that the key bottleneck to parallel decoding arises from the sequential certainty convergence for masked tokens. Building on this insight, we introduce the core of our approach: certainty-forcing distillation, a novel training strategy that distills the model to follow its original sampling trajectories while enforcing it to achieve high certainty on masked tokens more rapidly and in parallel. Extensive experiments across various benchmarks demonstrate that our method can dramatically reduce the number of decoding steps while maintaining performance. When applied to the LLaDA-8B-Instruct model, dParallel reduces decoding steps from 256 to 30 on GSM8K, achieving an 8.5x speedup without performance degradation. On the MBPP benchmark, it cuts decoding steps from 256 to 24, resulting in a 10.5x speedup while maintaining accuracy. Our code is available at https://github.com/czg1225/dParallel

Vision-Language-Action (VLA) models adapt large vision-language backbones to map images and instructions into robot actions. However, prevailing VLAs either generate actions auto-regressively in a fixed left-to-right order or attach separate MLP or diffusion heads outside the backbone, leading to fragmented information pathways and specialized training requirements that hinder a unified, scalable architecture. We present Discrete Diffusion VLA, a unified-transformer policy that models discretized action chunks with discrete diffusion. The design retains diffusion's progressive refinement paradigm while remaining natively compatible with the discrete token interface of VLMs. Our method achieves an adaptive decoding order that resolves easy action elements before harder ones and uses secondary re-masking to revisit uncertain predictions across refinement rounds, which improves consistency and enables robust error correction. This unified decoder preserves pre-trained vision-language priors, supports parallel decoding, breaks the autoregressive bottleneck, and reduces the number of function evaluations. Discrete Diffusion VLA achieves 96.3% avg. success rates on LIBERO, 71.2% visual matching on SimplerEnv-Fractal and 54.2% overall on SimplerEnv-Bridge. We also provide ablation study on vision-language ability retention on LIBERO-OOD (Out-of-Distribution) benchmark, with our method improving over autoregressive, MLP decoder and continuous diffusion baselines. These findings indicate that discrete-diffusion VLA supports precise action modeling and consistent training, laying groundwork for scaling VLA to larger models and datasets. Our code is available at https://github.com/Liang-ZX/DiscreteDiffusionVLA/tree/libero.

Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV) caching, and incoherent generation arising from learning dependencies over an intractable space of token combinations. To address these limitations, we introduce ReFusion, a novel masked diffusion model that achieves superior performance and efficiency by elevating parallel decoding from the token level to a higher slot level, where each slot is a fixed-length, contiguous sub-sequence. This is achieved through an iterative ``plan-and-infill''decoding process: a diffusion-based planning step first identifies a set of weakly dependent slots, and an autoregressive infilling step then decodes these selected slots in parallel. The slot-based design simultaneously unlocks full KV cache reuse with a unified causal framework and reduces the learning complexity from the token combination space to a manageable slot-level permutation space. Extensive experiments on seven diverse benchmarks show that ReFusion not only overwhelmingly surpasses prior MDMs with 34% performance gains and an over 18$\times$ speedup on average, but also bridges the performance gap to strong ARMs while maintaining a 2.33$\times$ average speedup.

Fast Automatic Speech Recognition (ASR) is critical for latency-sensitive applications such as real-time captioning and meeting transcription. However, truly parallel ASR decoding remains challenging due to the sequential nature of autoregressive (AR) decoders and the context limitations of non-autoregressive (NAR) methods. While modern ASR encoders can process up to 30 seconds of audio at once, AR decoders still generate tokens sequentially, creating a latency bottleneck. We propose Whisfusion, the first framework to fuse a pre-trained Whisper encoder with a text diffusion decoder. This NAR architecture resolves the AR latency bottleneck by processing the entire acoustic context in parallel at every decoding step. A lightweight cross-attention adapter trained via parameter-efficient fine-tuning (PEFT) bridges the two modalities. We also introduce a batch-parallel, multi-step decoding strategy that improves accuracy by increasing the number of candidates with minimal impact on speed. Fine-tuned solely on LibriSpeech (960h), Whisfusion achieves a lower WER than Whisper-tiny (8.3% vs. 9.7%), and offers comparable latency on short audio. For longer utterances (>20s), it is up to 2.6x faster than the AR baseline, establishing a new, efficient operating point for long-form ASR. The implementation and training scripts are available at https://github.com/taeyoun811/Whisfusion.

Multi-token generation has emerged as a promising paradigm for accelerating transformer-based large model inference. Recent efforts primarily explore diffusion Large Language Models (dLLMs) for parallel decoding to reduce inference latency. To achieve AR-level generation quality, many techniques adapt AR models into dLLMs to enable parallel decoding. However, they suffer from limited speedup compared to AR models due to a pretrain-to-posttrain mismatch. Specifically, the masked data distribution in post-training deviates significantly from the real-world data distribution seen during pretraining, and dLLMs rely on bidirectional attention, which conflicts with the causal prior learned during pretraining and hinders the integration of exact KV cache reuse. To address this, we introduce Jacobi Forcing, a progressive distillation paradigm where models are trained on their own generated parallel decoding trajectories, smoothly shifting AR models into efficient parallel decoders while preserving their pretrained causal inference property. The models trained under this paradigm, Jacobi Forcing Model, achieves 3.8x wall-clock speedup on coding and math benchmarks with minimal loss in performance. Based on Jacobi Forcing Models'trajectory characteristics, we introduce multi-block decoding with rejection recycling, which enables up to 4.5x higher token acceptance count per iteration and nearly 4.0x wall-clock speedup, effectively trading additional compute for lower inference latency. Our code is available at https://github.com/hao-ai-lab/JacobiForcing.

Diffusion Large Language Models (dLLMs) have demonstrated significant potential for high-speed inference. However, current confidence-driven decoding strategies are constrained by limited parallelism, typically achieving only 1--3 tokens per forward pass (TPF). In this work, we identify that the degree of parallelism during dLLM inference is highly sensitive to the Token Filling Order (TFO). Then, we introduce Lookahead PArallel Decoding LoPA, a training-free, plug-and-play algorithm, to identify a superior TFO and hence accelerate inference. LoPA concurrently explores distinct candidate TFOs via parallel branches, and selects the one with the highest potential for future parallelism based on branch confidence. We apply LoPA to the state-of-the-art D2F model and observe a substantial enhancement in decoding efficiency. Notably, LoPA increases the TPF of D2F-Dream to 10.1 on the GSM8K while maintaining performance superior to the Dream baseline. Furthermore, to facilitate this unprecedented degree of parallelism, we develop a specialized multi-device inference system featuring Branch Parallelism (BP), which achieves a single-sample throughput of 1073.9 tokens per second under multi-GPU deployment. The code is available at https://github.com/zhijie-group/LoPA.

Diffusion Language Models (DLMs) present a promising non-sequential paradigm for text generation, distinct from standard autoregressive (AR) approaches. However, current decoding strategies often adopt a reactive stance, underutilizing the global bidirectional context to dictate global trajectories. To address this, we propose Plan-Verify-Fill (PVF), a training-free paradigm that grounds planning via quantitative validation. PVF actively constructs a hierarchical skeleton by prioritizing high-leverage semantic anchors and employs a verification protocol to operationalize pragmatic structural stopping where further deliberation yields diminishing returns. Extensive evaluations on LLaDA-8B-Instruct and Dream-7B-Instruct demonstrate that PVF reduces the Number of Function Evaluations (NFE) by up to 65% compared to confidence-based parallel decoding across benchmark datasets, unlocking superior efficiency without compromising accuracy.

Diffusion-based Large Language Models (dLLMs) have emerged as a competitive alternative to autoregressive models, offering unique advantages through bidirectional attention and parallel generation paradigms. However, the generation results of current parallel decoding methods deviate from stepwise decoding, introducing potential performance degradation, which limits their practical deployment. To address this problem, we propose \textbf{S}elf \textbf{S}peculative \textbf{D}ecoding (SSD), a lossless inference acceleration method that leverages the dLLM itself as both speculative decoding drafter and verifier without auxiliary modules. SSD introduces a self-drafting mechanism where the model generates predictions for multiple positions, then verifies them through hierarchical verification trees in a single forward pass. Unlike traditional speculative decoding that requires separate draft models, SSD eliminates model redundancy and memory overhead by exploiting the dLLM's inherent parallel prediction capability for multiple positions. This self-speculative approach allows the model to progressively verify and accept multiple tokens in a single forward pass. Our experiments demonstrate that SSD achieves up to 3.46$\times$ speedup while keeping the output identical to stepwise decoding on open source models such as LLaDA and Dream. Code will be made publicly available on GitHub.

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

Speculative decoding has emerged as a widely adopted method to accelerate large language model inference without sacrificing the quality of the model outputs. While this technique has facilitated notable speed improvements by enabling parallel sequence verification, its efficiency remains inherently limited by the reliance on incremental token generation in existing draft models. To overcome this limitation, this paper proposes an adaptation of speculative decoding which uses discrete diffusion models to generate draft sequences. This allows parallelization of both the drafting and verification steps, providing significant speedups to the inference process. Our proposed approach, $\textit{Speculative Diffusion Decoding (SpecDiff)}$, is validated on standard language generation benchmarks and empirically demonstrated to provide up to 7.2x speedups over standard generation processes and up to 1.75x speedups over existing speculative decoding approaches.

Autoregressive (AR) models remain the standard for natural language generation but still suffer from high latency due to strictly sequential decoding. Recent diffusion-inspired approaches, such as LlaDA and Dream, mitigate this by generating in parallel, yet they suffer from two core limitations: information loss, as predictive distributions for non-finalized tokens are discarded at each step, and premature commitment, where local decisions are made without sufficient global coordination. We introduce Latent Refinement Decoding (LRD), a two-stage framework with Latent Refinement and a Predictive Feedback Loop. The first stage maintains masked positions as distributional mixtures of predicted tokens and the mask embedding, allowing the model to establish more globally consistent beliefs. The second stage progressively finalizes confident tokens while retaining uncertain ones for iterative feedback. KL-divergence dynamics provide a principled and reliable criterion for convergence and early stopping. Experiments across coding (HumanEval +6.3, MBPP +2.6) and reasoning (GSM8K +2.9, MATH500 +3.8) show that LRD improves accuracy while delivering speedups of up to 10.6x, making it a strong and versatile alternative for parallel sequence generation.

Diffusion Large Language Models (dLLMs) offer fast, parallel token generation, but their standalone use is plagued by an inherent efficiency-quality tradeoff. We show that, if carefully applied, the attributes of dLLMs can actually be a strength for drafters in speculative decoding with autoregressive (AR) verifiers. Our core insight is that dLLM's speed from parallel decoding drastically lowers the risk of costly rejections, providing a practical mechanism to effectively realize the (elusive) lengthy drafts that lead to large speedups with speculative decoding. We present FailFast, a dLLM-based speculative decoding framework that realizes this approach by dynamically adapting its speculation length. It"fails fast"by spending minimal compute in hard-to-speculate regions to shrink speculation latency and"wins big"by aggressively extending draft lengths in easier regions to reduce verification latency (in many cases, speculating and accepting 70 tokens at a time!). Without any fine-tuning, FailFast delivers lossless acceleration of AR LLMs and achieves up to 4.9$\times$ speedup over vanilla decoding, 1.7$\times$ over the best naive dLLM drafter, and 1.7$\times$ over EAGLE-3 across diverse models and workloads. We open-source FailFast at https://github.com/ruipeterpan/failfast.

Autoregressive (AR) language models generate text one token at a time, which limits their inference speed. Diffusion-based language models offer a promising alternative, as they can decode multiple tokens in parallel. However, we identify a key bottleneck in current diffusion LMs: the long decoding-window problem, where tokens generated far from the input context often become irrelevant or repetitive. Previous solutions like semi-autoregressive address this issue by splitting windows into blocks (sacrificing bidirectionality), but we find that this also leads to time-interval expansion problem, sacrificing the speed. Therefore, semi-AR eliminates the main advantages of diffusion models. To overcome this, we propose Convolutional decoding (Conv), a normalization-based method that narrows the decoding window without hard segmentation, leading to better fluency and flexibility. Additionally, we introduce Rejecting Rule-based Fine-Tuning (R2FT), a post-hoc training scheme that better aligns tokens at positions far from context. Our methods achieve state-of-the-art results on open-ended generation benchmarks (e.g., AlpacaEval) among diffusion LM baselines, with significantly lower step size than previous works, demonstrating both speed and quality improvements.

Autoregressive large language models achieve strong results on many benchmarks, but decoding remains fundamentally latency-limited by sequential dependence on previously generated tokens. Diffusion language models (DLMs) promise parallel generation but suffer from a fundamental static-to-dynamic misalignment: Training optimizes local transitions under fixed schedules, whereas efficient inference requires adaptive"long-jump"refinements through unseen states. Our goal is to enable highly parallel decoding for DLMs with low number of function evaluations while preserving generation quality. To achieve this, we propose CD4LM, a framework that decouples training from inference via Discrete-Space Consistency Distillation (DSCD) and Confidence-Adaptive Decoding (CAD). Unlike standard objectives, DSCD trains a student to be trajectory-invariant, mapping diverse noisy states directly to the clean distribution. This intrinsic robustness enables CAD to dynamically allocate compute resources based on token confidence, aggressively skipping steps without the quality collapse typical of heuristic acceleration. On GSM8K, CD4LM matches the LLaDA baseline with a 5.18x wall-clock speedup; across code and math benchmarks, it strictly dominates the accuracy-efficiency Pareto frontier, achieving a 3.62x mean speedup while improving average accuracy. Code is available at https://github.com/yihao-liang/CDLM

Diffusion Large Language Models (dLLMs) offer a compelling paradigm for natural language generation, leveraging parallel decoding and bidirectional attention to achieve superior global coherence compared to autoregressive models. While recent works have accelerated inference via KV cache reuse or heuristic decoding, they overlook the intrinsic inefficiencies within the block-wise diffusion process. Specifically, they suffer from spatial redundancy by modeling informative-sparse suffix regions uniformly and temporal inefficiency by applying fixed denoising schedules across all the decoding process. To address this, we propose Streaming-dLLM, a training-free framework that streamlines inference across both spatial and temporal dimensions. Spatially, we introduce attenuation guided suffix modeling to approximate the full context by pruning redundant mask tokens. Temporally, we employ a dynamic confidence aware strategy with an early exit mechanism, allowing the model to skip unnecessary iterations for converged tokens. Extensive experiments show that Streaming-dLLM achieves up to 68.2X speedup while maintaining generation quality, highlighting its effectiveness in diffusion decoding. The code is available at https://github.com/xiaoshideta/Streaming-dLLM.

Diffusion language models (DLMs) have recently emerged as a strong alternative to autoregressive models by enabling parallel text generation. To improve inference efficiency and KV-cache compatibility, prior work commonly adopts block-based diffusion, decoding tokens block by block. However, this paradigm suffers from a structural limitation that we term Boundary-Induced Context Truncation (BICT): undecoded tokens near block boundaries are forced to commit without access to nearby future context, even when such context could substantially reduce uncertainty. This limitation degrades decoding certainty and generation quality, especially for tasks requiring precise reasoning, such as mathematical problem solving and code generation. We propose Deferred Commitment Decoding (DCD), a novel, training-free decoding strategy that mitigates this issue. DCD maintains a certainty-aware sliding window over masked tokens, resolving low-uncertainty tokens early while deferring high-uncertainty tokens until sufficient contextual evidence becomes available. Extensive experiments across multiple diffusion language models, benchmarks, and caching configurations show that DCD improves generation accuracy by 1.73% with comparable time on average compared to fixed block-based diffusion methods, with the most significant improvement reaching 16.5%. These results demonstrate that deferring token commitment based on uncertainty is a simple yet effective principle for improving both the quality and efficiency of diffusion language model decoding.

Generative recommendation represents each item as a semantic ID, i.e., a sequence of discrete tokens, and generates the next item through autoregressive decoding. While effective, existing autoregressive models face two intrinsic limitations: (1) unidirectional constraints, where causal attention restricts each token to attend only to its predecessors, hindering global semantic modeling; and (2) error accumulation, where the fixed left-to-right generation order causes prediction errors in early tokens to propagate to the predictions of subsequent token. To address these issues, we propose LLaDA-Rec, a discrete diffusion framework that reformulates recommendation as parallel semantic ID generation. By combining bidirectional attention with the adaptive generation order, the approach models inter-item and intra-item dependencies more effectively and alleviates error accumulation. Specifically, our approach comprises three key designs: (1) a parallel tokenization scheme that produces semantic IDs for bidirectional modeling, addressing the mismatch between residual quantization and bidirectional architectures; (2) two masking mechanisms at the user-history and next-item levels to capture both inter-item sequential dependencies and intra-item semantic relationships; and (3) an adapted beam search strategy for adaptive-order discrete diffusion decoding, resolving the incompatibility of standard beam search with diffusion-based generation. Experiments on three real-world datasets show that LLaDA-Rec consistently outperforms both ID-based and state-of-the-art generative recommenders, establishing discrete diffusion as a new paradigm for generative recommendation.

Language models with recurrent depth, also referred to as universal or looped when considering transformers, are defined by the capacity to increase their computation through the repetition of layers. Recent efforts in pretraining have demonstrated that these architectures can scale to modern language modeling tasks while exhibiting advantages in reasoning tasks. In this work, we examine the relationship between recurrent-depth models and diffusion language models. Building on their similarities, we develop a new diffusion forcing sampler for these models to accelerate generation. The sampler advances by decoding new tokens at every forward pass of the model, while the latent states of these tokens can be further refined in parallel through recurrence. Theoretically, generation with our sampler is strictly more expressive than the baseline autoregressive generation using the same time budget on modern hardware. Moreover, this sampler, based on principles from diffusion literature, can be directly applied to existing 3.5B recurrent-depth transformers without any tuning, leading to up to a 5x speedup. Consequently, our findings not only provide an efficient mechanism for parallelizing the extra computation in recurrent-depth models at inference, but also suggest that such models can be naturally viewed as strong continuous, though causal, diffusion language models.

Speculative decoding is an effective and lossless approach for accelerating LLM inference. However, existing widely adopted model-based draft designs, such as EAGLE3, improve accuracy at the cost of multi-step autoregressive inference, resulting in high drafting latency and ultimately rendering the drafting stage itself a performance bottleneck. Inspired by diffusion-based large language models (dLLMs), we propose DART, which leverages parallel generation to reduce drafting latency. DART predicts logits for multiple future masked positions in parallel within a single forward pass based on hidden states of the target model, thereby eliminating autoregressive rollouts in the draft model while preserving a lightweight design. Based on these parallel logit predictions, we further introduce an efficient tree pruning algorithm that constructs high-quality draft token trees with N-gram-enforced semantic continuity. DART substantially reduces draft-stage overhead while preserving high draft accuracy, leading to significantly improved end-to-end decoding speed. Experimental results demonstrate that DART achieves a 2.03x--3.44x wall-clock time speedup across multiple datasets, surpassing EAGLE3 by 30% on average and offering a practical speculative decoding framework. Code is released at https://github.com/fvliang/DART.

We present Seed Diffusion Preview, a large-scale language model based on discrete-state diffusion, offering remarkably fast inference speed. Thanks to non-sequential, parallel generation, discrete diffusion models provide a notable speedup to mitigate the inherent latency of token-by-token decoding, as demonstrated recently (e.g., Mercury Coder, Gemini Diffusion). Seed Diffusion Preview achieves an inference speed of 2,146 token/s over H20 GPUs while maintaining competitive performance across a sweep of standard code evaluation benchmarks, significantly faster than contemporary Mercury and Gemini Diffusion, establishing new state of the art on the speed-quality Pareto frontier for code models.

Diffusion Large Language Models (DLLMs) have emerged as a compelling alternative to Autoregressive models, designed for fast parallel generation. However, existing DLLMs are plagued by a severe quality-speed trade-off, where faster parallel decoding leads to significant performance degradation. We attribute this to the irreversibility of standard decoding in DLLMs, which is easily polarized into the wrong decoding direction along with early error context accumulation. To resolve this, we introduce Wide-In, Narrow-Out (WINO), a training-free decoding algorithm that enables revokable decoding in DLLMs. WINO employs a parallel draft-and-verify mechanism, aggressively drafting multiple tokens while simultaneously using the model's bidirectional context to verify and re-mask suspicious ones for refinement. Verified in open-source DLLMs like LLaDA and MMaDA, WINO is shown to decisively improve the quality-speed trade-off. For instance, on the GSM8K math benchmark, it accelerates inference by 6$\times$ while improving accuracy by 2.58%; on Flickr30K captioning, it achieves a 10$\times$ speedup with higher performance. More comprehensive experiments are conducted to demonstrate the superiority and provide an in-depth understanding of WINO.

The capabilities of large language models (LLMs) are widely regarded as relying on autoregressive models (ARMs). We challenge this notion by introducing LLaDA, a diffusion model trained from scratch under the pre-training and supervised fine-tuning (SFT) paradigm. LLaDA employs a forward data masking process and a reverse generation process, parameterized by a Transformer to predict masked tokens. It provides a principled generative approach for probabilistic inference by optimizing a likelihood lower bound. Across extensive benchmarks on general tasks, math, code, and so on, LLaDA demonstrates strong scalability and performs comparably to our self-constructed ARM baselines. Remarkably, LLaDA 8B is competitive with strong LLMs like LLaMA3 8B in in-context learning and, after SFT, exhibits impressive instruction-following abilities in case studies such as multi-turn dialogue. Moreover, LLaDA addresses the reversal curse, surpassing GPT-4o in a reversal poem completion task. Our findings show the promise of diffusion models for language modeling at scale and challenge the common assumption that core LLM capabilities discussed above inherently depend on ARMs. Project page and codes: https://ml-gsai.github.io/LLaDA-demo/.

While Masked Diffusion Models (MDMs), such as LLaDA, present a promising paradigm for language modeling, there has been relatively little effort in aligning these models with human preferences via reinforcement learning. The challenge primarily arises from the high variance in Evidence Lower Bound (ELBO)-based likelihood estimates required for preference optimization. To address this issue, we propose Variance-Reduced Preference Optimization (VRPO), a framework that formally analyzes the variance of ELBO estimators and derives bounds on both the bias and variance of preference optimization gradients. Building on this theoretical foundation, we introduce unbiased variance reduction strategies, including optimal Monte Carlo budget allocation and antithetic sampling, that significantly improve the performance of MDM alignment. We demonstrate the effectiveness of VRPO by applying it to LLaDA, and the resulting model, LLaDA 1.5, outperforms its SFT-only predecessor consistently and significantly across mathematical (GSM8K +4.7), code (HumanEval +3.0, MBPP +1.8), and alignment benchmarks (IFEval +4.0, Arena-Hard +4.3). Furthermore, LLaDA 1.5 demonstrates a highly competitive mathematical performance compared to strong language MDMs and ARMs. Project page: https://ml-gsai.github.io/LLaDA-1.5-Demo/.

In this work, we introduce LLaDA-V, a purely diffusion-based Multimodal Large Language Model (MLLM) that integrates visual instruction tuning with masked diffusion models, representing a departure from the autoregressive paradigms dominant in current multimodal approaches. Built upon LLaDA, a representative large language diffusion model, LLaDA-V incorporates a vision encoder and MLP connector that projects visual features into the language embedding space, enabling effective multimodal alignment. Our empirical investigation reveals several intriguing results: First, LLaDA-V demonstrates promising multimodal performance despite its language model being weaker on purely textual tasks than counterparts like LLaMA3-8B and Qwen2-7B. When trained on the same instruction data, LLaDA-V is highly competitive to LLaMA3-V across multimodal tasks with better data scalability. It also narrows the performance gap to Qwen2-VL, suggesting the effectiveness of its architecture for multimodal tasks. Second, LLaDA-V achieves state-of-the-art performance in multimodal understanding compared to existing hybrid autoregressive-diffusion and purely diffusion-based MLLMs. Our findings suggest that large language diffusion models show promise in multimodal contexts and warrant further investigation in future research. Project page and codes: https://ml-gsai.github.io/LLaDA-V-demo/.

We present a novel encoder-only Transformer model for symbolic music harmony generation, based on a fixed time-grid representation of melody and harmony. Inspired by denoising diffusion processes, our model progressively unmasks harmony tokens over a sequence of discrete stages, learning to reconstruct the full harmonic structure from partial context. Unlike autoregressive models, this formulation enables flexible, non-sequential generation and supports explicit control over harmony placement. The model is stage-aware, receiving timestep embeddings analogous to diffusion timesteps, and is conditioned on both a binary piano roll and a pitch class roll to capture melodic context. We explore two unmasking schedules—random token revealing and midpoint doubling—both requiring a fixed and significantly reduced number of model calls at inference time. While our approach achieves competitive performance with strong autoregressive baselines (GPT-2 and BART) across several harmonic metrics, its key advantages lie in controllability, structured decoding with fixed inference steps, and alignment with musical structure. Ablation studies further highlight the role of stage awareness and pitch class conditioning. Our results position this method as a viable and interpretable alternative for symbolic harmony generation and a foundation for future work on structured, controllable musical modeling.

The rapid progress of auto-regressive vision-language models (VLMs) has inspired growing interest in vision-language-action models (VLA) for robotic manipulation. Recently, masked diffusion models, a paradigm distinct from autoregressive models, have begun to demonstrate competitive performance in text generation and multimodal applications, leading to the development of a series of diffusion-based VLMs (d-VLMs). However, leveraging such models for robot policy learning remains largely unexplored. In this work, we present LLaDA-VLA, the first Vision-Language-Diffusion-Action model built upon pretrained d-VLMs for robotic manipulation. To effectively adapt d-VLMs to robotic domain, we introduce two key designs: (1) a localized special-token classification strategy that replaces full-vocabulary classification with special action token classification, reducing adaptation difficulty; (2) a hierarchical action-structured decoding strategy that decodes action sequences hierarchically considering the dependencies within and across actions. Extensive experiments demonstrate that LLaDA-VLA significantly outperforms state-of-the-art VLAs on both simulation and real-world robots.

Diffusion large language models (dLLMs) are compelling alternatives to autoregressive (AR) models because their denoising models operate over the entire sequence. The global planning and iterative refinement features of dLLMs are particularly useful for code generation. However, current training and inference mechanisms for dLLMs in coding are still under-explored. To demystify the decoding behavior of dLLMs and unlock their potential for coding, we systematically investigate their denoising processes and reinforcement learning (RL) methods. We train a 7B dLLM, \textbf{DiffuCoder}, on 130B tokens of code. Using this model as a testbed, we analyze its decoding behavior, revealing how it differs from that of AR models: (1) dLLMs can decide how causal their generation should be without relying on semi-AR decoding, and (2) increasing the sampling temperature diversifies not only token choices but also their generation order. This diversity creates a rich search space for RL rollouts. For RL training, to reduce the variance of token log-likelihood estimates and maintain training efficiency, we propose \textbf{coupled-GRPO}, a novel sampling scheme that constructs complementary mask noise for completions used in training. In our experiments, coupled-GRPO significantly improves DiffuCoder's performance on code generation benchmarks (+4.4\% on EvalPlus) and reduces reliance on AR bias during decoding. Our work provides deeper insight into the machinery of dLLM generation and offers an effective, diffusion-native RL training framework. https://github.com/apple/ml-diffucoder.

We present DiffusionBERT, a new generative masked language model based on discrete dif- fusion models. Diffusion models and many pre- trained language models have a shared training objective, i.e., denoising, making it possible to combine the two powerful models and enjoy the best of both worlds. On the one hand, dif- fusion models offer a promising training strat- egy that helps improve the generation quality. On the other hand, pre-trained denoising lan- guage models (e.g., BERT) can be used as a good initialization that accelerates convergence. We explore training BERT to learn the reverse process of a discrete diffusion process with an absorbing state and elucidate several designs to improve it. First, we propose a new noise schedule for the forward diffusion process that controls the degree of noise added at each step based on the information of each token. Sec- ond, we investigate several designs of incorpo- rating the time step into BERT. Experiments on unconditional text generation demonstrate that DiffusionBERT achieves significant improve- ment over existing diffusion models for text (e.g., D3PM and Diffusion-LM) and previous generative masked language models in terms of perplexity and BLEU score. Promising re- sults in conditional generation tasks show that DiffusionBERT can generate texts of compa- rable quality and more diverse than a series of established baselines.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.75 (CIFAR-10) and 3.40 (ImageNet 64x64) bits per dimension that are better than autoregressive models of similar sizes. Our code is available at https://github.com/google-deepmind/md4.

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from MDMs has been scarcely explored. We make the observation that often a given sequence of partially masked tokens determines the values of multiple unknown tokens deterministically, meaning that a single prediction of a masked model holds additional information unused by standard sampling procedures. Based on this observation, we introduce EB-Sampler, a simple drop-in replacement for existing samplers, utilizing an Entropy Bounded unmasking procedure that dynamically unmasks multiple tokens in one function evaluation with predefined approximate error tolerance. We formulate the EB-Sampler as part of a broad family of adaptive samplers for which we provide an error analysis that motivates our algorithmic choices. EB-Sampler accelerates sampling from current state of the art MDMs by roughly 2-3x on standard coding and math reasoning benchmarks without loss in performance. We also validate the same procedure works well on smaller reasoning tasks including maze navigation and Sudoku, tasks ARMs often struggle with.

End-to-end autonomous driving systems built on Vision Language Models (VLMs) have shown significant promise, yet their reliance on autoregressive architectures introduces some limitations for real-world applications. The sequential, token-by-token generation process of these models results in high inference latency and cannot perform bidirectional reasoning, making them unsuitable for dynamic, safety-critical environments. To overcome these challenges, we introduce ViLaD, a novel Large Vision Language Diffusion (LVLD) framework for end-to-end autonomous driving that represents a paradigm shift. ViLaD leverages a masked diffusion model that enables parallel generation of entire driving decision sequences, significantly reducing computational latency. Moreover, its architecture supports bidirectional reasoning, allowing the model to consider both past and future simultaneously, and supports progressive easy-first generation to iteratively improve decision quality. We conduct comprehensive experiments on the nuScenes dataset, where ViLaD outperforms state-of-the-art autoregressive VLM baselines in both planning accuracy and inference speed, while achieving a near-zero failure rate. Furthermore, we demonstrate the framework's practical viability through a real-world deployment on an autonomous vehicle for an interactive parking task, confirming its effectiveness and soundness for practical applications.

Autoregressive models (ARMs) have long dominated the landscape of biomedical vision-language models (VLMs). Recently, masked diffusion models such as LLaDA have emerged as promising alternatives, yet their application in the biomedical domain remains largely underexplored. To bridge this gap, we introduce LLaDA-MedV, the first large language diffusion model tailored for biomedical image understanding through vision instruction tuning. LLaDA-MedV achieves relative performance gains of 7.855% over LLaVA-Med and 1.867% over LLaDA-V in the open-ended biomedical visual conversation task, and sets new state-of-the-art accuracy on the closed-form subset of three VQA benchmarks: 84.93% on VQA-RAD, 92.31% on SLAKE, and 95.15% on PathVQA. Furthermore, a detailed comparison with LLaVA-Med suggests that LLaDA-MedV is capable of generating reasonably longer responses by explicitly controlling response length, which can lead to more informative outputs. We also conduct an in-depth analysis of both the training and inference stages, highlighting the critical roles of initialization weight selection, fine-tuning strategies, and the interplay between sampling steps and response repetition. The code and model weight is released at https://github.com/LLM-VLM-GSL/LLaDA-MedV.

We present a masked diffusion language modeling framework for data-efficient training for the BabyLM 2025 Challenge. Our approach applies diffusion training objectives to language modeling under strict data constraints, incorporating frequency-informed masking that prioritizes learning from rare tokens while maintaining theoretical validity. We explore multiple noise scheduling strategies, including two-mode approaches, and investigate different noise weighting schemes within the NELBO objective. We evaluate our method on the BabyLM benchmark suite, measuring linguistic competence, world knowledge, and human-likeness. Results show performance competitive to hybrid autoregressive-masked baselines, demonstrating that diffusion-based training offers a viable alternative for data-restricted language learning.

Tree search has recently emerged as a powerful framework for aligning generative models with task-specific rewards at test time. Applying tree search to Masked Diffusion Language Models, however, introduces two key challenges: (i) parallel unmasking yields highly correlated branches, limiting exploration, and (ii) reward evaluation via sampled completions produces high-variance estimates, making pruning unstable. We propose TReASURe, a tree-search test-time alignment method that addresses these issues. It introduces (i) UnmaskBranch, a branching strategy based on first-hitting unmasking that diversifies both token content and reveal order with a single model call per parent node, and (ii) ResubstituteScore, a pruning rule that uses deterministic resubstitution to score partially masked sequences with low-variance proxy completions. Theoretically, we quantify branching efficiency gains in NFEs (number of function evaluations), show that the scoring rule approximates the true reward with error bounded by predictive uncertainty, and prove improvements with larger tree widths. Empirically, TReASURe achieves state-of-the-art results on perplexity, linguistic acceptability, and control of sentiment and toxicity, outperforming prior methods under matched compute budgets, with especially strong gains in low-NFE regimes.

Masked diffusion language models (MDLMs) generate text via iterative masked-token denoising, enabling mask-parallel decoding and distinct controllability and efficiency tradeoffs from autoregressive LLMs. Yet, efficient representation-level mechanisms for inference-time control in MDLMs remain largely unexplored. To address this gap, we introduce an activation steering primitive for MDLMs: we extract a single low-dimensional direction from contrastive prompt sets using one prompt-only forward pass, and apply a global intervention on residual-stream activations throughout reverse diffusion, without performing optimization or altering the diffusion sampling procedure. Using safety refusal as a deployment-relevant case study, we find that refusal behavior in multiple MDLMs is governed by a consistent, approximately one-dimensional activation subspace. Applying the corresponding direction yields large and systematic behavioral shifts and is substantially more effective than prompt-based and optimization-based baselines. We further uncover diffusion-specific accessibility: effective directions can be extracted not only from post-instruction tokens, but also from pre-instruction tokens that are typically ineffective in autoregressive models due to causal attention. Ablations localize maximal leverage to early denoising steps and mid-to-late transformer layers, with early diffusion blocks contributing disproportionately. Finally, in an MDLM trained on English and Chinese, extracted directions transfer strongly between English and Chinese, but do not reliably generalize to an autoregressive architecture, highlighting architecture-dependent representations of safety constraints.

Diffusion models have demonstrated strong potential in language modeling, offering various advantages over traditional autoregressive approaches. Their ability to generate and revise entire responses in parallel enables faster generation and built-in self-correction mechanisms. Most modern diffusion-based language models employ masked diffusion, where decoding involves iteratively processing masked tokens based on a binary decision: either retaining the mask or replacing it with the predicted token. However, this binary choice discards valuable predictive information when the mask is retained. To address this limitation, we introduce soft-masking (SM), a novel method that dynamically blends the embedding of the mask token with the embeddings of the top-k predicted tokens from the previous decoding step, for each retained mask. This provides the model with a more informative prior, preserving context from earlier computations and allowing partial information about masked tokens to propagate beyond a single step. We propose a training methodology that efficiently adapts masked diffusion language models to incorporate SM. We demonstrate that training a 169M parameter model from scratch with SM yields superior perplexity and MAUVE scores compared to binary masking baselines. Similarly, a pretrained model can be enhanced with SM through continued pretraining. Finally, we finetune two state-of-the-art diffusion models, Dream-7B and Dream-Coder-7B, with SM. SM consistently improves performance across multiple coding benchmarks, particularly in high-throughput settings. The code is available at https://github.com/IBM/soft-masked-diffusion-language-models.

Masked diffusion language models (MDMs) have recently gained traction as a viable generative framework for natural language. This can be attributed to its scalability and ease of training compared to other diffusion model paradigms for discrete data, establishing itself as the state-of-the-art non-autoregressive generator for discrete data. Diffusion models, in general, have shown excellent ability to improve the generation quality by leveraging inference-time scaling either by increasing the number of denoising steps or by using external verifiers on top of the outputs of each step to guide the generation. In this work, we propose a verifier-based inference-time scaling method that aids in finding a better candidate generation during the denoising process of the MDM. Our experiments demonstrate the application of MDMs for standard text-style transfer tasks and establish MDMs as a better alternative to autoregressive language models. Additionally, we show that a simple soft-value-based verifier setup for MDMs using off-the-shelf pre-trained embedding models leads to significant gains in generation quality even when used on top of typical classifier-free guidance setups in the existing literature.

Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent in their parallelism remain largely unexplored. To this end, we characterize what types of reasoning problems MDMs can provably solve and how efficiently. We do this by connecting MDMs to the well-understood reasoning frameworks of chain of thought (CoT) and padded looped transformers (PLTs) in the finite-precision log-width setting: We show that MDMs and polynomially-padded PLTs are, in fact, equivalent in this setting, and that MDMs can solve all problems that CoT-augmented transformers can. Moreover, we showcase classes of problems (including regular languages) for which MDMs are inherently more efficient than CoT transformers, where parallel generation allows for substantially faster reasoning.

Electroencephalogram (EEG)-to-text remains challenging due to high-dimensional noise, subject variability, and error accumulation in autoregressive decoding. We introduce DELTA, which pairs a Residual Vector Quantization (RVQ) EEG tokenizer with a masked language diffusion model (LLaDA). RVQ discretizes continuous EEG into multi-layer tokens to reduce noise and individual differences, while LLaDA reconstructs sentences via non-sequential denoising. On ZuCo, DELTA improves semantic alignment by up to 5.37 points over autoregressive baselines, achieving BLEU-1 21.9 and ROUGE-1 F 17.2 under word-level conditions. These results enable reliable text generation from small EEG-text datasets and point toward scalable multimodal EEG-language models.

Vision-Language Models (VLMs) have achieved remarkable progress in multimodal reasoning and generation, yet their high computational demands remain a major challenge. Diffusion Vision-Language Models (DVLMs) are particularly attractive because they enable parallel token decoding, but the large number of visual tokens still significantly hinders their inference efficiency. While visual token pruning has been extensively studied for autoregressive VLMs (AVLMs), it remains largely unexplored for DVLMs. In this work, we propose RedVTP, a response-driven visual token pruning strategy that leverages the inference dynamics of DVLMs. Our method estimates visual token importance using attention from the masked response tokens. Based on the observation that these importance scores remain consistent across steps, RedVTP prunes the less important visual tokens from the masked tokens after the first inference step, thereby maximizing inference efficiency. Experiments show that RedVTP improves token generation throughput of LLaDA-V and LaViDa by up to 186% and 28.05%, respectively, and reduces inference latency by up to 64.97% and 21.87%, without compromising-and in some cases improving-accuracy.

Masked diffusion models have demonstrated competitive results on various tasks including language generation. However, due to its iterative refinement process, the inference is often bottlenecked by slow and static sampling speed. To overcome this problem, we introduce `KL-Adaptive Stability Sampling'(KLASS), a fast yet effective sampling method that exploits token-level KL divergence to identify stable, high-confidence predictions. By unmasking multiple tokens in each iteration without any additional model training, our approach speeds up generation significantly while maintaining sample quality. On reasoning benchmarks, KLASS achieves up to $2.78\times$ wall-clock speedups while improving performance over standard greedy decoding, attaining state-of-the-art results among diffusion-based samplers. We further validate KLASS across diverse domains, including text, image, and molecular generation, showing its effectiveness as a broadly applicable sampler across different models.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20$\times$ speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs in text generation. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that it lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

Autoregressive Models (ARMs) have long dominated the landscape of Large Language Models. Recently, a new paradigm has emerged in the form of diffusion-based Large Language Models (dLLMs), which generate text by iteratively denoising masked segments. This approach has shown significant advantages and potential. However, dLLMs suffer from high inference latency. Traditional ARM acceleration techniques, such as Key-Value caching, are incompatible with dLLMs due to their bidirectional attention mechanism. To address this specific challenge, our work begins with a key observation that dLLM inference involves a static prompt and a partially dynamic response, where most tokens remain stable across adjacent denoising steps. Based on this, we propose dLLM-Cache, a training-free adaptive caching framework that combines long-interval prompt caching with partial response updates guided by feature similarity. This design enables efficient reuse of intermediate computations without compromising model performance. Extensive experiments on representative dLLMs, including LLaDA 8B and Dream 7B, show that dLLM-Cache achieves up to 9.1 x speedup over standard inference without compromising output quality. Notably, our method brings dLLM inference latency close to that of ARMs under many settings. Codes are provided in the supplementary material and will be released publicly on GitHub.

A major bottleneck of standard auto-regressive large language models is that their inference process is inherently sequential, resulting in very long and costly inference times. To circumvent this, practitioners proposed a class of language models called diffusion language models, of which the masked diffusion model (MDM) is the most successful. The MDM is able to sample tokens out-of-order and, ostensibly, many tokens at once and in parallel. However, there is very limited rigorous understanding of how much parallel sampling these models can perform without noticeable degradation in their sampling performance. Prior work of Li and Cai obtained some preliminary bounds, but these are not tight for many natural classes of distributions. In this work, we give a new, exact characterization of the expected divergence between the true distribution and the sampled distribution, for any distribution and any unmasking schedule for the sampler, showing an elegant connection to the theory of univariate function approximation. By leveraging this connection, we then attain a number of novel lower and upper bounds for this problem. While the connection to function approximation in principle gives the optimal unmasking schedule for any distribution, we show that it is in general impossible to compete with it without strong a priori knowledge of the distribution, even in seemingly benign settings. However, we also demonstrate new upper bounds and new sampling schedules in terms of well-studied information-theoretic properties of the base distribution, namely, its total correlation and dual total correlation, which show that in some natural settings, one can sample in $O(log n)$ steps without any visible loss in performance, where $n$ is the total sequence length.

Large language models (LLMs) predominantly use autoregressive (AR) approaches, but masked diffusion models (MDMs) are emerging as viable alternatives. A key challenge in comparing AR and MDM paradigms is their typical architectural difference: AR models are often decoder-only, while MDMs have largely been encoder-only. This practice of changing both the modeling paradigm and architecture simultaneously makes direct comparisons unfair, as it's hard to distinguish whether observed differences stem from the paradigm itself or the architectural shift. This research evaluates MDMs within a decoder-only framework to: (1) equitably compare MDM (as Any-Order AR, or AO-AR) and standard AR paradigms. Our investigation suggests that the standard AO-AR objective, which averages over all token permutations, may benefit from refinement, as many permutations appear less informative compared to the language's inherent left-to-right structure. (2) Investigate architectural influences (decoder-only vs. encoder-only) within MDMs. We demonstrate that while encoder-only MDMs model a simpler conditional probability space, decoder-only MDMs can achieve dramatic generation speedups ($\sim25\times$) and comparable perplexity with temperature annealing despite modeling a vastly larger space, highlighting key trade-offs. This work thus decouples core paradigm differences from architectural influences, offering insights for future model design. Code is available at https://github.com/scxue/AO-GPT-MDM.

Masked diffusion language models (MDLMs) are trained to in-fill positions in randomly masked sequences, in contrast to next-token prediction models. Discussions around MDLMs focus on two benefits: (1) any-order decoding and 2) multi-token decoding. However, we observe that for math and coding tasks, any-order algorithms often underperform or behave similarly to left-to-right sampling, and standard multi-token decoding significantly degrades performance. At inference time, MDLMs compute the conditional distribution of all masked positions. A natural question is: How can we justify this additional compute when left-to-right one-token-at-a-time decoding is on par with any-order decoding algorithms? First, we propose reasoning-as-infilling. By using MDLMs to infill a reasoning template, we can structure outputs and distinguish between reasoning and answer tokens. In turn, this enables measuring answer uncertainty during reasoning, and early exits when the model converges on an answer. Next, given an answer, reasoning-as-infilling enables sampling from the MDLM posterior over reasoning traces conditioned on the answer, providing a new source of high-quality data for post-training. On GSM8k, we observe that fine-tuning LLaDA-8B Base on its posterior reasoning traces provides a performance boost on par with fine-tuning on human-written reasoning traces. Additionally, given an answer, reasoning-as-infilling provides a method for scoring the correctness of the reasoning process at intermediate steps. Second, we propose multi-token entropy decoding (MED), a simple adaptive sampler that minimizes the error incurred by decoding positions in parallel based on the conditional entropies of those positions. MED preserves performance across benchmarks and leads to 2.7x fewer steps. Our work demonstrates that the training and compute used by MDLMs unlock many new inference and post-training methods.

Masked diffusion models (MDMs) offer a promising non-autoregressive alternative for large language modeling. Standard decoding methods for MDMs, such as confidence-based sampling, select tokens independently based on individual token confidences at each diffusion step. However, we observe that this independent token selection often results in generation orders resembling sequential autoregressive processes, limiting the advantages of non-autoregressive modeling. To mitigate this pheonomenon, we propose Reward-Weighted Sampling (RWS), a novel decoding strategy that leverages an external reward model to provide a principled global signal during the iterative diffusion process. Specifically, at each diffusion step, RWS evaluates the quality of the entire intermediate sequence and scales token logits accordingly, guiding token selection by integrating global sequence-level coherence. This method selectively increases the confidence of tokens that initially have lower scores, thereby promoting a more non-autoregressive generation order. Furthermore, we provide theoretical justification showing that reward-weighted logit scaling induces beneficial rank reversals in token selection and consistently improves expected reward. Experiments demonstrate that RWS significantly promotes non-autoregressive generation orders, leading to improvements across multiple evaluation metrics. These results highlight the effectiveness of integrating global signals in enhancing both the non-autoregressive properties and overall performance of MDMs.

No abstract available

Generative recommendation (GR) with semantic IDs (SIDs) has emerged as a promising alternative to traditional recommendation approaches due to its performance gains, capitalization on semantic information provided through language model embeddings, and inference and storage efficiency. Existing GR with SIDs works frame the probability of a sequence of SIDs corresponding to a user's interaction history using autoregressive modeling. While this has led to impressive next item prediction performances in certain settings, these autoregressive GR with SIDs models suffer from expensive inference due to sequential token-wise decoding, potentially inefficient use of training data and bias towards learning short-context relationships among tokens. Inspired by recent breakthroughs in NLP, we propose to instead model and learn the probability of a user's sequence of SIDs using masked diffusion. Masked diffusion employs discrete masking noise to facilitate learning the sequence distribution, and models the probability of masked tokens as conditionally independent given the unmasked tokens, allowing for parallel decoding of the masked tokens. We demonstrate through thorough experiments that our proposed method consistently outperforms autoregressive modeling. This performance gap is especially pronounced in data-constrained settings and in terms of coarse-grained recall, consistent with our intuitions. Moreover, our approach allows the flexibility of predicting multiple SIDs in parallel during inference while maintaining superior performance to autoregressive modeling.

Recently, Masked Diffusion Models (MDMs) have shown promising potential across vision, language, and cross-modal generation. However, a notable discrepancy exists between their training and inference procedures. In particular, MDM inference is a multi-step, iterative process governed not only by the model itself but also by various schedules that dictate the token-decoding trajectory (e.g., how many tokens to decode at each step). In contrast, MDMs are typically trained using a simplified, single-step BERT-style objective that masks a subset of tokens and predicts all of them simultaneously. This step-level simplification fundamentally disconnects the training paradigm from the trajectory-level nature of inference, leaving the inference schedules never optimized during training. In this paper, we introduce Co-GRPO, which reformulates MDM generation as a unified Markov Decision Process (MDP) that jointly incorporates both the model and the inference schedule. By applying Group Relative Policy Optimization at the trajectory level, Co-GRPO cooperatively optimizes model parameters and schedule parameters under a shared reward, without requiring costly backpropagation through the multi-step generation process. This holistic optimization aligns training with inference more thoroughly and substantially improves generation quality. Empirical results across four benchmarks-ImageReward, HPS, GenEval, and DPG-Bench-demonstrate the effectiveness of our approach. For more details, please refer to our project page: https://co-grpo.github.io/ .

Autoregressive language models dominate modern text generation, yet their sequential nature introduces fundamental limitations: decoding is slow, and maintaining global coherence remains challenging. Diffusion models offer a promising alternative by enabling parallel generation and flexible control; however, their application to text generation is hindered by the high dimensionality of token-level representations. We introduce Cosmos, a novel approach to text generation that operates entirely in a compressed, smooth latent space tailored specifically for diffusion. This space is learned using an autoencoder trained simultaneously for token-level reconstruction and alignment with frozen activations from a pretrained language encoder, providing robust semantic grounding and enabling effective perturbation-based augmentations. Empirically, we demonstrate that text representations can be compressed by $8\times$ while maintaining generation quality comparable to token-level diffusion models. Furthermore, increasing the latent sequence length allows Cosmos to surpass both diffusion-based and autoregressive baselines. We evaluate Cosmos on four diverse generative tasks including story generation, question generation, summarization, and detoxification and compare it with various generative paradigms. Cosmos achieves comparable or superior generation quality while offering more than $2\times$ faster inference. Code is released at \href{https://github.com/MeshchaninovViacheslav/cosmos}{GitHub}

Large Language Models (LLMs) demonstrate their reasoning ability through chain-of-thought (CoT) generation. However, LLM's autoregressive decoding may limit the ability to revisit and refine earlier tokens in a holistic manner, which can also lead to inefficient exploration for diverse solutions. In this paper, we propose LaDiR (Latent Diffusion Reasoner), a novel reasoning framework that unifies the expressiveness of continuous latent representation with the iterative refinement capabilities of latent diffusion models for an existing LLM. We first construct a structured latent reasoning space using a Variational Autoencoder (VAE) that encodes text reasoning steps into blocks of thought tokens, preserving semantic information and interpretability while offering compact but expressive representations. Subsequently, we utilize a latent diffusion model that learns to denoise a block of latent thought tokens with a blockwise bidirectional attention mask, enabling longer horizon and iterative refinement with adaptive test-time compute. This design allows efficient parallel generation of diverse reasoning trajectories, allowing the model to plan and revise the reasoning process holistically. We conduct evaluations on a suite of mathematical reasoning and planning benchmarks. Empirical results show that LaDiR consistently improves accuracy, diversity, and interpretability over existing autoregressive, diffusion-based, and latent reasoning methods, revealing a new paradigm for text reasoning with latent diffusion.

Diffusion Large Language Models (DLLMs) are inherently ill-suited for variable-length generation, as their inference is defined on a fixed-length canvas and implicitly assumes a known target length. When the length is unknown, as in realistic completion and infilling, naively comparing confidence across mask lengths becomes systematically biased, leading to under-generation or redundant continuations. In this paper, we show that this failure arises from an intrinsic lengthinduced bias in generation confidence estimates, leaving existing DLLMs without a robust way to determine generation length and making variablelength inference unreliable. To address this issue, we propose LR-DLLM, a length-regularized inference framework for DLLMs that treats generation length as an explicit variable and achieves reliable length determination at inference time. It decouples semantic compatibility from lengthinduced uncertainty through an explicit length regularization that corrects biased confidence estimates. Based on this, LR-DLLM enables dynamic expansion or contraction of the generation span without modifying the underlying DLLM or its training procedure. Experiments show that LRDLLM achieves 51.3% Pass@1 on HumanEvalInfilling under fully unknown lengths (+13.4% vs. DreamOn) and 51.5% average Pass@1 on four-language McEval (+14.3% vs. DreamOn).

We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for training EBM, by replacing Markov Chain Monte Carlo (MCMC) distribution with a trainable sampler, such as a diffusion model. In GCD, the joint training of EBM and a diffusion model is formulated as a minimax problem, which reaches an equilibrium when both models converge to the data distribution. The minimax learning with GCD bears interesting equivalence to inverse reinforcement learning, where the energy corresponds to a negative reward, the diffusion model is a policy, and the real data is expert demonstrations. We present preliminary yet promising results showing that joint training is beneficial for both EBM and a diffusion model. GCD enables EBM training without MCMC while improving the sample quality of a diffusion model.

In this paper, we introduce a novel dIffusion language modEl pre-training framework for text generation, which we call GENIE. GENIE is a large-scale pretrained diffusion language model that consists of an encoder and a diffusion-based decoder, which can generate text by gradually transforming a random noise sequence into a coherent text sequence. To pre-train GENIE on a large-scale language corpus, we design a new continuous paragraph denoise objective, which encourages the diffusion-decoder to reconstruct a clean text paragraph from a corrupted version, while preserving the semantic and syntactic coherence. We evaluate GENIE on four downstream text generation benchmarks, namely XSum, CNN/DailyMail, Gigaword, and CommonGen. Our experimental results show that GENIE achieves comparable performance with the state-of-the-art autoregressive models on these benchmarks, and generates more diverse text samples. The code and models of GENIE are available at https://github.com/microsoft/ProphetNet/tree/master/GENIE.

Recent advances in diffusion models have set an impressive milestone in many generation tasks, and trending works such as DALL-E2, Imagen, and Stable Diffusion have attracted great interest. Despite the rapid landscape changes, recent new approaches focus on extensions and performance rather than capacity, thus requiring separate models for separate tasks. In this work, we expand the existing single-flow diffusion pipeline into a multi-task multimodal network, dubbed Versatile Diffusion (VD), that handles multiple flows of text-to-image, image-to-text, and variations in one unified model. The pipeline design of VD instantiates a unified multi-flow diffusion framework, consisting of sharable and swappable layer modules that enable the crossmodal generality beyond images and text. Through extensive experiments, we demonstrate that VD successfully achieves the following: a) VD outperforms the baseline approaches and handles all its base tasks with competitive quality; b) VD enables novel extensions such as disentanglement of style and semantics, dual- and multi-context blending, etc.; c) The success of our multi-flow multimodal framework over images and text may inspire further diffusion-based universal AI research. Our code and models are open-sourced at https://github.com/SHI-Labs/Versatile-Diffusion.

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a \textit{symmetry conjecture} that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), supported by empirical evidence. This negative correlation leads to substantially more reliable uncertainty quantification with up to $90\%$ narrower confidence intervals. We demonstrate these gains on tasks including estimating pixel-wise statistics and evaluating diffusion inverse solvers. We also provide extensions with randomized quasi-Monte Carlo noise designs for uncertainty quantification, and explore additional applications of the antithetic noise design to improve image editing and generation diversity. Our framework is training-free, model-agnostic, and adds no runtime overhead. Code is available at https://github.com/jjia131/Antithetic-Noise-in-Diffusion-Models-page.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

Generative learning, recognized for its effective modeling of data distributions, offers inherent advantages in handling out-of-distribution instances, especially for enhancing robustness to adversarial attacks. Among these, diffusion classifiers, utilizing powerful diffusion models, have demonstrated superior empirical robustness. However, a comprehensive theoretical understanding of their robustness is still lacking, raising concerns about their vulnerability to stronger future attacks. In this study, we prove that diffusion classifiers possess $O(1)$ Lipschitzness, and establish their certified robustness, demonstrating their inherent resilience. To achieve non-constant Lipschitzness, thereby obtaining much tighter certified robustness, we generalize diffusion classifiers to classify Gaussian-corrupted data. This involves deriving the evidence lower bounds (ELBOs) for these distributions, approximating the likelihood using the ELBO, and calculating classification probabilities via Bayes' theorem. Experimental results show the superior certified robustness of these Noised Diffusion Classifiers (NDCs). Notably, we achieve over 80% and 70% certified robustness on CIFAR-10 under adversarial perturbations with \(\ell_2\) norms less than 0.25 and 0.5, respectively, using a single off-the-shelf diffusion model without any additional data.

Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al. (2022) introduced the first framework for continuous-time discrete diffusion. However, their training and sampling processes differ significantly from the discrete-time version, necessitating nontrivial approximations for tractability. In this paper, we first present a series of mathematical simplifications of the variational lower bound that enable more accurate and easy-to-optimize training for discrete diffusion. In addition, we derive a simple formulation for backward denoising that enables exact and accelerated sampling, and importantly, an elegant unification of discrete-time and continuous-time discrete diffusion. Thanks to simpler analytical formulations, both forward and now also backward probabilities can flexibly accommodate any noise distribution, including different noise distributions for multi-element objects. Experiments show that our proposed USD3 (for Unified Simplified Discrete Denoising Diffusion) outperform all SOTA baselines on established datasets. We open-source our unified code at https://github.com/LingxiaoShawn/USD3.

Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schrödinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not directly apply to discrete diffusion. Here, we provide a straightforward derivation of classifier-free and classifier-based guidance for discrete diffusion, as well as a new class of diffusion models that leverage uniform noise and that are more guidable because they can continuously edit their outputs. We improve the quality of these models with a novel continuous-time variational lower bound that yields state-of-the-art performance, especially in settings involving guidance or fast generation. Empirically, we demonstrate that our guidance mechanisms combined with uniform noise diffusion improve controllable generation relative to autoregressive and diffusion baselines on several discrete data domains, including genomic sequences, small molecule design, and discretized image generation.

It is encouraged to see that progress has been made to bridge videos and natural language. However, mainstream video captioning methods suffer from slow inference speed due to the sequential manner of autoregressive decoding, and prefer generating generic descriptions due to the insufficient training of visual words (e.g., nouns and verbs) and inadequate decoding paradigm. In this paper, we propose a non-autoregressive decoding based model with a coarse-to-fine captioning procedure to alleviate these defects. In implementations, we employ a bi-directional self-attention based network as our language model for achieving inference speedup, based on which we decompose the captioning procedure into two stages, where the model has different focuses. Specifically, given that visual words determine the semantic correctness of captions, we design a mechanism of generating visual words to not only promote the training of scene-related words but also capture relevant details from videos to construct a coarse-grained sentence "template". Thereafter, we devise dedicated decoding algorithms that fill in the "template" with suitable words and modify inappropriate phrasing via iterative refinement to obtain a fine-grained description. Extensive experiments on two mainstream video captioning benchmarks, i.e., MSVD and MSR-VTT, demonstrate that our approach achieves state-of-the-art performance, generates diverse descriptions, and obtains high inference efficiency. Our code is available at https://github.com/yangbang18/Non-Autoregressive-Video-Captioning.

We investigate a fully Latent AutoRegressive scheme based on a Gaussian Process (GP) integrated into a Variational Autoencoder (VAE). In this setting, sequential dynamics are transferred from the observation space to a continuous latent space, while linguistic generation remains parallel through a non-autoregressive decoder. We present a complete methodological formulation, including a causal GP prior, a structured amortized posterior, and a training protocol based on a regularized ELBO. Empirical evaluation, conducted within a deliberately constrained proof-of-concept (POC) framework, shows that the model can be trained stably and that the sequential and parallel sampling variants exhibit consistent behavior. Overall, the results suggest that part of the temporal structure in a language model can be supported by the probabilistic geometry of the latent space rather than by explicit neural operations.

Diffusion models have garnered considerable interest in the field of text generation. Several studies have explored text diffusion models with different structures and applied them to various tasks, including named entity recognition and summarization. However, there exists a notable disparity between the "easy-first" text generation process of current diffusion models and the "keyword-first" natural text generation process of humans, which has received limited attention. To bridge this gap, we propose InfoDiffusion, a non-autoregressive text diffusion model. Our approach introduces a "keyinfo-first" generation strategy and incorporates a noise schedule based on the amount of text information. In addition, InfoDiffusion combines self-conditioning with a newly proposed partially noising model structure. Experimental results show that InfoDiffusion outperforms the baseline model in terms of generation quality and diversity, as well as exhibiting higher sampling efficiency.

Despite the non-autoregressive potential of diffusion language models (dLLMs), existing decoding strategies demonstrate positional bias, failing to fully unlock the potential of arbitrary generation. In this work, we delve into the inherent spectral characteristics of dLLMs and present the first frequency-domain analysis showing that low-frequency components in hidden states primarily encode global structural information and long-range dependencies, while high-frequency components are responsible for characterizing local details. Based on this observation, we propose FourierSampler, which leverages a frequency-domain sliding window mechanism to dynamically guide the model to achieve a "structure-to-detail" generation. FourierSampler outperforms other inference enhancement strategies on LLADA and SDAR, achieving relative improvements of 20.4% on LLaDA1.5-8B and 16.0% on LLaDA-8B-Instruct. It notably surpasses similarly sized autoregressive models like Llama3.1-8B-Instruct.

While pre-trained language models have achieved great success on various natural language understanding tasks, how to effectively leverage them into non-autoregressive generation tasks remains a challenge. To solve this problem, we present a non-autoregressive generation model based on pre-trained transformer models. To bridge the gap between autoregressive and non-autoregressive models, we propose a simple and effective iterative training method called MIx Source and pseudo Target (MIST). Unlike other iterative decoding methods, which sacrifice the inference speed to achieve better performance based on multiple decoding iterations, MIST works in the training stage and has no effect on inference time. Our experiments on three generation benchmarks including question generation, summarization and paraphrase generation, show that the proposed framework achieves the new state-of-the-art results for fully non-autoregressive models. We also demonstrate that our method can be used to a variety of pre-trained models. For instance, MIST based on the small pre-trained model also obtains comparable performance with seq2seq models.

We introduce Diffusion-based Audio Captioning (DAC), a non-autoregressive diffusion model tailored for diverse and efficient audio captioning. Although existing captioning models relying on language backbones have achieved remarkable success in various captioning tasks, their insufficient performance in terms of generation speed and diversity impede progress in audio understanding and multimedia applications. Our diffusion-based framework offers unique advantages stemming from its inherent stochasticity and holistic context modeling in captioning. Through rigorous evaluation, we demonstrate that DAC not only achieves SOTA performance levels compared to existing benchmarks in the caption quality, but also significantly outperforms them in terms of generation speed and diversity. The success of DAC illustrates that text generation can also be seamlessly integrated with audio and visual generation tasks using a diffusion backbone, paving the way for a unified, audio-related generative model across different modalities.

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Masked diffusion language models generate by iteratively filling masked tokens over multiple denoising steps, so learning only from a terminal reward on the final completion yields coarse credit assignment over intermediate decisions. We propose DiSPO (Diffusion-State Policy Optimization), a plug-in credit-assignment layer that directly optimizes intermediate filling decisions. At selected intermediate masked states, DiSPO branches by resampling fillings for the currently masked positions from rollout-cached logits, scores the resulting completions, and updates only the newly filled tokens -- without additional multi-step diffusion rollouts. We formalize a fixed-state objective for branched completions and derive a policy-gradient estimator that can be combined with terminal-feedback policy optimization using the same rollouts. On LLaDA-8B-Instruct, DiSPO consistently improves over the terminal-feedback diffu-GRPO baseline on math and planning benchmarks under matched rollout compute and optimizer steps. Our code will be available at https://daioba.github.io/dispo .

Diffusion Language Models (DLMs) offer a promising alternative for language modeling by enabling parallel decoding through iterative refinement. However, most DLMs rely on hard binary masking and discrete token assignments, which hinder the revision of early decisions and underutilize intermediate probabilistic representations. In this paper, we propose EvoToken-DLM, a novel diffusion-based language modeling approach that replaces hard binary masks with evolving soft token distributions. EvoToken-DLM enables a progressive transition from masked states to discrete outputs, supporting revisable decoding. To effectively support this evolution, we introduce continuous trajectory supervision, which aligns training objectives with iterative probabilistic updates. Extensive experiments across multiple benchmarks show that EvoToken-DLM consistently achieves superior performance, outperforming strong diffusion-based and masked DLM baselines. Project webpage: https://aim-uofa.github.io/EvoTokenDLM.

This paper presents a novel training method, Conditional Masked Language Modeling (CMLM), to effectively learn sentence representations on large scale unlabeled corpora. CMLM integrates sentence representation learning into MLM training by conditioning on the encoded vectors of adjacent sentences. Our English CMLM model achieves state-of-the-art performance on SentEval, even outperforming models learned using supervised signals. As a fully unsupervised learning method, CMLM can be conveniently extended to a broad range of languages and domains. We find that a multilingual CMLM model co-trained with bitext retrieval (BR) and natural language inference (NLI) tasks outperforms the previous state-of-the-art multilingual models by a large margin, e.g. 10% improvement upon baseline models on cross-lingual semantic search. We explore the same language bias of the learned representations, and propose a simple, post-training and model agnostic approach to remove the language identifying information from the representation while still retaining sentence semantics.

We frame embedding inversion as conditional masked diffusion, recovering all tokens in parallel through iterative denoising rather than sequential autoregressive generation. A masked diffusion language model is conditioned on the target embedding via adaptive layer normalization, requiring only 8 forward passes with no access to the target encoder at inference time. On 32-token sequences across three embedding models, the method achieves token recovery through parallel denoising without requiring encoder access, iterative correction, or architecture-specific alignment. Source code and live demo are available at https://github.com/jina-ai/embedding-inversion-demo.

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts.