Daily Papers

Discrete masked diffusion language models support bidirectional generation and infilling, but adapting pretrained autoregressive (AR) transformers requires reconciling causal pretraining with bidirectional denoising. We study this problem at the level of attention rather than claiming AR-weight reuse itself as novel. PreDiff-LM preserves causal attention within the observed prompt while allowing full bidirectional attention within the masked target. Under a matched GPT-2 Medium, WikiText-103, 90K-step setup, this hybrid mask improves unconditional perplexity from 34.1 to 28.7 and MAUVE from 0.71 to 0.78 over uniform bidirectional attention with the same AR initialization. Attention adaptation also composes with a DiffuGPT-style objective adaptation, reaching 26.9 perplexity. Pretrained initialization reduces the steps required to reach perplexity below 50 from about 350K to 8K, although a compute-matched fine-tuned AR model remains stronger at equal scale (18.9 versus 28.7). Beyond perplexity, PreDiff-LM improves repetition, distributional quality, four zero-shot downstream tasks, and human preference over prior diffusion baselines. The results position hybrid attention as a complementary mechanism for adapting pretrained causal backbones, while making explicit the remaining quality and inference-efficiency gaps to optimized AR models.

Discrete Masked diffusion language models generate text by iterative parallel decoding, but few-step decoding suffers from a tradeoff between length and quality: with a fixed step budget, standard methods can generate a short, high-quality output, or they can produce long but repetitive text. Continuous denoising can sidestep this tradeoff by evolving all positions jointly in embedding space, but building such a model from scratch at scale remains an open problem. We show that a pretrained masked DLM can instead be lightly adapted to support continuous embedding-space denoising. Starting from LLaDA-8B-Instruct, we continue-pretrain for only 1,000 steps with Discrete Stochastic Localization (DSL), replacing binary masking with continuous per-token Gaussian noise as a soft mask. The adapted model supports continuous inference that evolves all positions jointly in embedding space and defers hard token commitment to the final step. On zero-shot summarization at low step budgets (<=16 forward passes), DSL-LLaDA-SDE achieves the best ROUGE-1 on all four benchmarks and largely avoids the premature-termination / repetition tradeoff of iterative unmasking. The same adaptation also yields selective noisy-state robustness: the model corrects corrupted tokens while preserving clean ones. Control experiments using standard masked diffusion training with the same compute demonstrate neither behavior.

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 release our code at: https://github.com/kuleshov-group/mdlm

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.

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.

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.

Diffusion language models, especially masked discrete diffusion models, have achieved great success recently. While there are some theoretical and primary empirical results showing the advantages of latent reasoning with looped transformers or continuous chain-of-thoughts, continuous diffusion models typically underperform their discrete counterparts. In this paper, we argue that diffusion language models do not necessarily need to be in the discrete space. In particular, we prove that continuous diffusion models have stronger expressivity than discrete diffusions and looped transformers. We attribute the contradiction between the theoretical expressiveness and empirical performance to their practical trainability: while continuous diffusion provides intermediate supervision that looped transformers lack, they introduce additional difficulty decoding tokens into the discrete token space from the continuous representation space. We therefore propose Coevolutionary Continuous Discrete Diffusion (CCDD), which defines a joint multimodal diffusion process on the union of a continuous representation space and a discrete token space, leveraging a single model to simultaneously denoise in the joint space. By combining two modalities, CCDD is expressive with rich semantics in the latent space, as well as good trainability and sample quality with the help of explicit discrete tokens. We also propose effective architectures and advanced training/sampling techniques for CCDD, which reveals strong empirical performance in extensive language modeling experiments on real-world tasks.

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

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.

Masked diffusion language models (MDLMs) generate text by iteratively unmasking tokens, but their standard decoder reduces each step to a binary action: a position is either committed to a single token or left fully masked, discarding rich predictive information rather than carrying it forward, and forcing premature, irrevocable commitments that lead to poor performance under a limited decoding budget. In this paper, we reinterpret mask prediction as a clean-state prediction (x-prediction) and show that it can be used to induce a continuous flow in the input embedding space. Building on this view, we propose a continuous decoding framework for MDLMs where tokens can accumulate partial progress at each diffusion step and remain revisable. To match the uneven contextual constraints across positions in language, we replace the globally synchronous schedule in image diffusion with a confidence-based asynchronous update in which the diffusion progress is token-wise accumulated. Additionally, we introduce a lightweight policy network and formulate its training as a reinforcement learning problem. Applied to pretrained LLaDA, our decoder retains 83--97% of full-budget accuracy using under 15% of the diffusion steps, largely outperforming discrete mask-prediction decoding at matched budgets.

In discrete generative modeling, two dominant paradigms demonstrate divergent capabilities: Masked Diffusion Language Models (MDLM) excel at semantic understanding and zero-shot generalization, whereas Uniform-noise Diffusion Language Models (UDLM) achieve strong few-step generation quality, yet neither attains balanced performance across both dimensions. To address this, we propose XDLM, which bridges the two paradigms via a stationary noise kernel. XDLM offers two key contributions: (1) it provides a principled theoretical unification of MDLM and UDLM, recovering each paradigm as a special case; and (2) an alleviated memory bottleneck enabled by an algebraic simplification of the posterior probabilities. Experiments demonstrate that XDLM advances the Pareto frontier between understanding capability and generation quality. Quantitatively, XDLM surpasses UDLM by 5.4 points on zero-shot text benchmarks and outperforms MDLM in few-step image generation (FID 54.1 vs. 80.8). When scaled to tune an 8B-parameter large language model, XDLM achieves 15.0 MBPP in just 32 steps, effectively doubling the baseline performance. Finally, analysis of training dynamics reveals XDLM's superior potential for long-term scaling. Code is available at https://github.com/MzeroMiko/XDLM

Early DNA foundation models adopted BERT-style training, achieving good performance on DNA understanding tasks but lacking generative capabilities. Recent autoregressive models enable DNA generation, but employ left-to-right causal modeling that is suboptimal for DNA where regulatory relationships are inherently bidirectional. We present D3LM (Discrete DNA Diffusion Language Model), which unifies bidirectional representation learning and DNA generation through masked diffusion. D3LM directly adopts the Nucleotide Transformer (NT) v2 architecture but reformulates the training objective as masked diffusion in discrete DNA space, enabling both bidirectional understanding and generation capabilities within a single model. Compared to NT v2 of the same size, D3LM achieves improved performance on understanding tasks. Notably, on regulatory element generation, D3LM achieves an SFID of 10.92, closely approaching real DNA sequences (7.85) and substantially outperforming the previous best result of 29.16 from autoregressive models. Our work suggests diffusion language models as a promising paradigm for unified DNA foundation models. We further present the first systematic study of masked diffusion models in the DNA domain, investigating practical design choices such as tokenization schemes and sampling strategies, thereby providing empirical insights and a solid foundation for future research. D3LM has been released at https://huggingface.co/collections/Hengchang-Liu/d3lm.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the natural discrete substitute is not a deterministic trajectory but its stochastic counterpart: the exact posterior bridge, available in closed form for broad corruption families including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage, teacher-free training framework. A single CDLM objective unifies masked diffusion, continuous consistency models, and progressive/discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

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 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

End-to-end autonomous driving systems based on vision-language-action (VLA) models integrate multimodal sensor inputs and language instructions to generate planning and control signals. While autoregressive large language models and continuous diffusion policies are prevalent, the potential of discrete masked diffusion for trajectory generation remains largely unexplored. This paper presents WAM-Diff, a VLA framework that employs masked diffusion to iteratively refine a discrete sequence representing future ego-trajectories. Our approach features three key innovations: a systematic adaptation of masked diffusion for autonomous driving that supports flexible, non-causal decoding orders; scalable model capacity via a sparse MoE architecture trained jointly on motion prediction and driving-oriented visual question answering (VQA); and online reinforcement learning using Group Sequence Policy Optimization (GSPO) to optimize sequence-level driving rewards. Remarkably, our model achieves 91.0 PDMS on NAVSIM-v1 and 89.7 EPDMS on NAVSIM-v2, demonstrating the effectiveness of masked diffusion for autonomous driving. The approach provides a promising alternative to autoregressive and diffusion-based policies, supporting scenario-aware decoding strategies for trajectory generation. The code for this paper will be released publicly at: https://github.com/fudan-generative-vision/WAM-Diff

While state-of-the-art language models achieve impressive results through next-token prediction, they have inherent limitations such as the inability to revise already generated tokens. This has prompted exploration of alternative approaches such as discrete diffusion. However, masked diffusion, which has emerged as a popular choice due to its simplicity and effectiveness, reintroduces this inability to revise words. To overcome this, we generalize masked diffusion and derive the theoretical backbone of a family of general interpolating discrete diffusion (GIDD) processes offering greater flexibility in the design of the noising processes. Leveraging a novel diffusion ELBO, we achieve compute-matched state-of-the-art performance in diffusion language modeling. Exploiting GIDD's flexibility, we explore a hybrid approach combining masking and uniform noise, leading to improved sample quality and unlocking the ability for the model to correct its own mistakes, an area where autoregressive models notoriously have struggled. Our code and models are open-source: https://github.com/dvruette/gidd/

While recent multimodal large language models (MLLMs) have made impressive strides, they predominantly employ a conventional autoregressive architecture as their backbone, leaving significant room to explore effective and efficient alternatives in architectural design. Concurrently, recent studies have successfully applied discrete diffusion models to various domains, such as visual understanding and image generation, revealing their considerable potential as a promising backbone for multimodal systems. Drawing inspiration from these pioneering research, we introduce Omni-Diffusion, the first any-to-any multimodal language model built entirely on mask-based discrete diffusion models, which unifies understanding and generation across text, speech, and images. Omni-Diffusion employs a unified mask-based discrete diffusion model to directly capture the joint distribution over discrete multimodal tokens. This approach supports not only bimodal tasks but also more complex scenarios involving multiple modalities. On a diverse set of benchmarks, our method outperforms or performs on par with existing multimodal systems that process two or more modalities, highlighting the significant promise of diffusion models in powering the next generation of multimodal foundation models. Project webpage: https://omni-diffusion.github.io.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated K-step unrolling pipeline to learn multi-step dynamics. MetaState adds only {sim}0.6% trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5% across all evaluations.

Discrete diffusion language models (dLLMs) accelerate text generation by unmasking multiple tokens in parallel. However, parallel decoding introduces a distributional mismatch: it approximates the joint conditional using a fully factorized product of per-token marginals, which degrades output quality when selected tokens are strongly dependent. We propose DEMASK (DEpendency-guided unMASKing), a lightweight dependency predictor that attaches to the final hidden states of a dLLM. In a single forward pass, it estimates pairwise conditional influences between masked positions. Using these predictions, a greedy selection algorithm identifies positions with bounded cumulative dependency for simultaneous unmasking. Under a sub-additivity assumption, we prove this bounds the total variation distance between our parallel sampling and the model's joint. Empirically, DEMASK achieves 1.7-2.2times speedup on Dream-7B while matching or improving accuracy compared to confidence-based and KL-based baselines.

Discrete diffusion models have emerged as strong alternatives to autoregressive language models, with recent work initializing and fine-tuning a base unimodal model for bimodal generation. Diverging from previous approaches, we introduce the first tri-modal masked diffusion model pretrained from scratch on text, image-text, and audio-text data. We systematically analyze multimodal scaling laws, modality mixing ratios, noise schedules, and batch-size effects, and we provide optimized inference sampling defaults. Our batch-size analysis yields a novel stochastic differential equation (SDE)-based reparameterization that eliminates the need for tuning the optimal batch size as reported in recent work. This reparameterization decouples the physical batch size, often chosen based on compute constraints (GPU saturation, FLOP efficiency, wall-clock time), from the logical batch size, chosen to balance gradient variance during stochastic optimization. Finally, we pretrain a preliminary 3B-parameter tri-modal model on 6.4T tokens, demonstrating the capabilities of a unified design and achieving strong results in text generation, text-to-image tasks, and text-to-speech tasks. Our work represents the largest-scale systematic open study of multimodal discrete diffusion models conducted to date, providing insights into scaling behaviors across multiple modalities.

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.

We present Dynin-Omni, the first masked-diffusion-based omnimodal foundation model that unifies text, image, and speech understanding and generation, together with video understanding, within a single architecture. Unlike autoregressive unified models that serialize heterogeneous modalities, or compositional unified models that require orchestration with external modality-specific decoders, Dynin-Omni natively formulates omnimodal modeling as masked diffusion over a shared discrete token space, enabling iterative refinement under bidirectional context. Dynin-Omni adopts a multi-stage training strategy with model-merging-based modality expansion and omnimodal alignment. We evaluate Dynin-Omni across 19 multimodal benchmarks spanning language reasoning, image generation and editing, video understanding, and speech recognition and synthesis. Dynin-Omni achieves 87.6 on GSM8K, 1733.6 on MME-P, 61.4 on VideoMME, 0.87 on GenEval, and 2.1 WER on LibriSpeech test-clean, consistently outperforming existing open-source unified models while remaining competitive with strong modality-specific expert systems. These results demonstrate the potential of masked diffusion as a unified paradigm for any-to-any modeling, providing a flexible foundation for real-time omnimodal systems, unified cross-modal retrieval and generation, and embodied multimodal agents.

Masked diffusion models (MDMs) are a potential alternative to autoregressive models (ARMs) for language generation, but generation quality depends critically on the generation order. Prior work either hard-codes an ordering (e.g., blockwise left-to-right) or learns an ordering policy for a pretrained MDM, which incurs extra cost and can yield suboptimal solutions due to the two-stage optimization. Motivated by this, we propose order-expressive masked diffusion model (OeMDM) for a broad class of diffusion generative processes with various generation orders, enabling the interpretation of MDM, ARM, and block diffusion in a single framework. Furthermore, building on OeMDM, we introduce learnable-order masked diffusion model (LoMDM), which jointly learns the generation ordering and diffusion backbone through a single objective from scratch, enabling the diffusion model to generate text in context-dependent ordering. Empirically, we confirm that LoMDM outperforms various discrete diffusion models across multiple language modeling benchmarks.

Masked Diffusion Models (MDMs) provide an efficient non-causal alternative to autoregressive generation but often struggle with token dependencies and semantic incoherence due to their reliance on discrete marginal distributions. We address these limitations by shifting the diffusion process into a continuous sentence-level semantic space. We propose CRoCoDiL (Continuous and Robust Conditioned Diffusion for Language), a unified fine-tuning approach that jointly trains an encoder-demasker architecture, grounding the MDM demasking in continuous latent representations. This leads to the formation of a novel autoencoder in which decoding is obtained by an MDM algorithm. Relying on the same framework, we introduce two unconditional text synthesis algorithms: Continuous-Then-Discrete (ConThenDisc), a hybrid-diffusion approach that first generates latent representations in continuous space and then decodes these to tokens via an MDM, and Continuous-Within-Discrete (ConWithinDisc), a multi-diffusion strategy that refines latent representations throughout the discrete sampling process. Experiments using LLaDA show that our methods achieve superior generation quality and more than 10x faster sampling speeds in an unconditional setting.

We present DiffusionBERT, a new generative masked language model based on discrete diffusion 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, diffusion models offer a promising training strategy that helps improve the generation quality. On the other hand, pre-trained denoising language 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. Second, we investigate several designs of incorporating the time step into BERT. Experiments on unconditional text generation demonstrate that DiffusionBERT achieves significant improvement 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.

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 20times speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs. 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 the numerical issue 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.

The bifurcation of generative modeling into autoregressive approaches for discrete data (text) and diffusion approaches for continuous data (images) hinders the development of truly unified multimodal systems. While Masked Language Models (MLMs) offer efficient bidirectional context, they traditionally lack the generative fidelity of autoregressive models and the semantic continuity of diffusion models. Furthermore, extending masked generation to multimodal settings introduces severe alignment challenges and training instability. In this work, we propose CoM-DAD (Coupled Manifold Discrete Absorbing Diffusion), a novel probabilistic framework that reformulates multimodal generation as a hierarchical dual-process. CoM-DAD decouples high-level semantic planning from low-level token synthesis. First, we model the semantic manifold via a continuous latent diffusion process; second, we treat token generation as a discrete absorbing diffusion process, regulated by a Variable-Rate Noise Schedule, conditioned on these evolving semantic priors. Crucially, we introduce a Stochastic Mixed-Modal Transport strategy that aligns disparate modalities without requiring heavy contrastive dual-encoders. Our method demonstrates superior stability over standard masked modeling, establishing a new paradigm for scalable, unified text-image generation.

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

Discrete diffusion models have achieved success in tasks like image generation and masked language modeling but face limitations in controlled content editing. We introduce DICE (Discrete Inversion for Controllable Editing), the first approach to enable precise inversion for discrete diffusion models, including multinomial diffusion and masked generative models. By recording noise sequences and masking patterns during the reverse diffusion process, DICE enables accurate reconstruction and flexible editing of discrete data without the need for predefined masks or attention manipulation. We demonstrate the effectiveness of DICE across both image and text domains, evaluating it on models such as VQ-Diffusion, Paella, and RoBERTa. Our results show that DICE preserves high data fidelity while enhancing editing capabilities, offering new opportunities for fine-grained content manipulation in discrete spaces. For project webpage, see https://hexiaoxiao-cs.github.io/DICE/.

Fast and high-quality language generation is the holy grail that people pursue in the age of AI. In this work, we introduce Discrete Diffusion Divergence Instruct (DiDi-Instruct), a training-based method that initializes from a pre-trained (masked) discrete diffusion language model (dLLM) and distills a few-step student for fast generation. The resulting DiDi-Instruct model achieves comparable or superior performance to its dLLM teacher and the GPT-2 baseline while enabling up to 64times acceleration. The theoretical foundation of DiDi-Instruct is a novel framework based on integral KL-divergence minimization, which yields a practical training algorithm. We further introduce grouped reward normalization, intermediate-state matching, and the reward-guided ancestral sampler that significantly improve training stability, model coverage, and inference quality. On OpenWebText, DiDi-Instruct achieves perplexity from 62.2 (8 NFEs) to 18.4 (128 NFEs), which outperforms prior accelerated dLLMs and GPT-2 baseline. These gains come with a negligible entropy loss (around 1%) and reduce additional training wall-clock time by more than 20times compared to competing dLLM distillation methods. We further validate the robustness and effectiveness of DiDi-Instruct through extensive ablation studies, model scaling, and the generation of discrete protein sequences. In conclusion, DiDi-Instruct is an efficient yet effective distillation method, enabling language generation in the blink of an eye. We will release both code and models at github.com/haoyangzheng-ai/didi-instruct.

Masked discrete diffusion is a dominant paradigm for high-quality language modeling where tokens are iteratively corrupted to a mask state, yet its inference efficiency is bottlenecked by the lack of deterministic sampling tools. While diffusion duality enables deterministic distillation for uniform models, these approaches generally underperform masked models and rely on complex integral operators. Conversely, in the masked domain, prior methods typically assume the absence of deterministic trajectories, forcing a reliance on stochastic distillation. To bridge this gap, we establish explicit Masked Diffusion Duality, proving that the masked process arises as the projection of a continuous Gaussian process via a novel maximum-value index preservation mechanism. Furthermore, we introduce Masked Consistency Distillation (MCD), a principled framework that leverages this duality to analytically construct the deterministic coupled trajectories required for consistency distillation, bypassing numerical ODE solvers. This result strictly improves upon prior stochastic distillation methods, achieving a 16times inference speedup without compromising generation quality. Our findings not only provide a solid theoretical foundation connecting masked and continuous diffusion, but also unlock the full potential of consistency distillation for high-performance discrete generation. Our code is available at https://anonymous.4open.science/r/MCD-70FD.

Discrete Vision-Language-Action (VLA) models typically formulate action generation as next-token prediction over discretized action spaces, conditioning each token autoregressively on prior context. While effective, this paradigm incurs high inference latency and largely ignores the temporal structure inherent in action trajectories. Recent efforts introduce parallel decoding to improve efficiency, enabling faster inference, but lack explicit mechanisms for modeling token dependencies. We introduce TBD-VLA, a discrete token-based VLA framework that incorporates block diffusion to enable temporal action generation. We partition action sequences into temporal blocks and perform masked discrete diffusion within each block, while maintaining autoregressive generation across blocks. This design unifies temporal autoregression and parallel action decoding, achieving both strong temporal coherence and improved inference speed. In addition, the explicit temporal modeling enables asynchronous execution of action chunks (e.g., Real-Time Chunking) via temporal in-painting. TBD-VLA significantly outperforms prior VLA approaches in both simulation and real-world manipulation tasks, offering a scalable path toward fast, temporally aware, discrete VLA models. Project webpage: https://tbd-vla.github.io/

Peptide therapeutics, a major class of medicines, have achieved remarkable success across diseases such as diabetes and cancer, with landmark examples such as GLP-1 receptor agonists revolutionizing the treatment of type-2 diabetes and obesity. Despite their success, designing peptides that satisfy multiple conflicting objectives, such as target binding affinity, solubility, and membrane permeability, remains a major challenge. Classical drug development and structure-based design are ineffective for such tasks, as they fail to optimize global functional properties critical for therapeutic efficacy. Existing generative frameworks are largely limited to continuous spaces, unconditioned outputs, or single-objective guidance, making them unsuitable for discrete sequence optimization across multiple properties. To address this, we present PepTune, a multi-objective discrete diffusion model for the simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with state-dependent masking schedules and penalty-based objectives. To guide the diffusion process, we propose a Monte Carlo Tree Search (MCTS)-based strategy that balances exploration and exploitation to iteratively refine Pareto-optimal sequences. MCTS integrates classifier-based rewards with search-tree expansion, overcoming gradient estimation challenges and data sparsity inherent to discrete spaces. Using PepTune, we generate diverse, chemically-modified peptides optimized for multiple therapeutic properties, including target binding affinity, membrane permeability, solubility, hemolysis, and non-fouling characteristics on various disease-relevant targets. In total, our results demonstrate that MCTS-guided discrete diffusion is a powerful and modular approach for multi-objective sequence design in discrete state spaces.

Vision-Language-Action (VLA) models aim to control robots for manipulation from visual observations and natural-language instructions. However, existing hierarchical and autoregressive paradigms often introduce architectural overhead, suffer from temporal inconsistency and long-horizon error accumulation, and lack a mechanism to capture environment dynamics without extra modules. To this end, we present MMaDA-VLA, a fully native pre-trained large diffusion VLA model that unifies multi-modal understanding and generation in a single framework. Our key idea is a native discrete diffusion formulation that embeds language, images, and continuous robot controls into one discrete token space and trains a single backbone with masked token denoising to jointly generate a future goal observation and an action chunk in parallel. Iterative denoising enables global, order-free refinement, improving long-horizon consistency while grounding actions in predicted future visual outcomes without auxiliary world models. Experiments across simulation benchmarks and real-world tasks show state-of-the-art performance, achieving 98.0% average success on LIBERO and 4.78 average length on CALVIN.

Diffusion models offer appealing properties for language generation, such as parallel decoding and iterative refinement, but the discrete and highly structured nature of text challenges the direct application of diffusion principles. In this paper, we revisit diffusion language modeling from the view of diffusion process and language modeling, and outline five properties that separate diffusion mechanics from language-specific requirements. We first categorize existing approaches into continuous diffusion in embedding space and discrete diffusion over tokens. We then show that each satisfies only part of the five essential properties and therefore reflects a structural trade-off. Through analyses of recent large diffusion language models, we identify two central issues: (i) uniform corruption does not respect how information is distributed across positions, and (ii) token-wise marginal training cannot capture multi-token dependencies during parallel decoding. These observations motivate diffusion processes that align more closely with the structure of text, and encourage future work toward more coherent diffusion language models.

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.

Diffusion language models (DLMs) have recently emerged as a compelling alternative to autoregressive generation, offering parallel generation and improved global coherence. During inference, DLMs generate text by iteratively denoising masked sequences in parallel; however, determining which positions to unmask and which tokens to commit forms a large combinatorial search problem. Existing inference methods approximate this search using heuristics, which often yield suboptimal decoding paths; other approaches instead rely on additional training to guide token selection. To introduce a principled search mechanism for DLMs inference, we introduce MEDAL, a framework that integrates Monte Carlo Tree SEarch initialization for Diffusion LAnguage Model inference. We employ Monte Carlo Tree Search at the initialization stage to explore promising unmasking trajectories, providing a robust starting point for subsequent refinement. This integration is enabled by restricting the search space to high-confidence actions and prioritizing token choices that improve model confidence over remaining masked positions. Across multiple benchmarks, MEDAL achieves up to 22.0% improvement over existing inference strategies, establishing a new paradigm for search-based inference in diffusion language models.

Diffusion models have recently been extended to language generation through Masked Diffusion Language Models (MDLMs), which achieve performance competitive with strong autoregressive models. However, MDLMs tend to degrade in the few-step regime and cannot directly adopt existing few-step distillation methods designed for continuous diffusion models, as they lack the intrinsic property of mapping from noise to data. Recent Uniform-state Diffusion Models (USDMs), initialized from a uniform prior, alleviate some limitations but still suffer from complex loss formulations that hinder scalability. In this work, we propose a simplified denoising-based loss for USDMs that optimizes only noise-replaced tokens, stabilizing training and matching ELBO-level performance. Furthermore, by framing denoising as self-supervised learning, we introduce a simple modification to our denoising loss with contrastive-inspired negative gradients, which is practical and yield additional improvements in generation quality.

Masked Diffusion Language Models (MDLMs) have recently emerged as a promising alternative to Autoregressive Language Models (ARLMs), leveraging a denoising objective that, in principle, should enable more uniform context utilisation. In this work, we examine the context comprehension abilities of MDLMs and uncover two key limitations. First, despite their more global training objective and bidirectional attention mechanism, similarly to ARLMS, MDLMs exhibit a strong locality bias: performance is highly sensitive to the position of relevant information within the input, favouring local over distant context. Second, we show that appending a large number of mask tokens--required for generation--can significantly degrade context comprehension. Through systematic ablations, we find that these masks act as distractors, reducing the model's ability to process relevant information. To address this, we introduce a mask-agnostic loss function that encourages predictions to remain invariant to the number of appended masks. Fine-tuning with this objective substantially mitigates the distracting effect of masks, improving robustness of MDLMs. Overall, our findings reveal critical limitations of the current MDLM training paradigm and provide actionable insights for building diffusion-based language models with stronger context comprehension.

Masked Diffusion Language Models (MDLMs) have emerged as a compelling non-autoregressive alternative to standard large language models; however, their application to morphologically rich languages remains limited. In this paper, we introduce Diffutron, a masked diffusion language model specifically designed for Turkish. Our approach leverages a resource-efficient training pipeline, starting with LoRA-based continual pre-training of a multilingual encoder on a large-scale corpus. To enable generative capabilities, we employ a progressive instruction-tuning strategy, sequentially adapting the model on general and task-specific instruction sets. Experimental results across comprehensive benchmarks demonstrate that, despite its compact size, our model achieves competitive performance compared to existing multi-billion-parameter baselines. These findings validate the effectiveness of masked diffusion modeling combined with multi-stage tuning for non-autoregressive text generation in Turkish.

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/

Masked diffusion language models (MDLMs) promise fast, non-autoregressive text generation, yet existing samplers, which pick tokens to unmask based on model confidence, ignore interactions when unmasking multiple positions in parallel and effectively reduce to slow, autoregressive behavior. We propose the Dilated Unmasking Scheduler (DUS), an inference-only, planner-model-free method that partitions sequence positions into non-adjacent dilated groups and unmasked them in parallel so as to minimize an upper bound on joint entropy gain at each denoising step. By explicitly trading off the number of network calls against generation quality, DUS recovers most of the performance lost under traditional parallel unmasking strategies. Across math (GSM8K, MATH500), code (HumanEval, MBPP) and general-knowledge benchmarks (BBH, MMLU-Pro), DUS outperforms confidence-based planners, without modifying the underlying denoiser, and reveals the true speed-quality frontier of MDLMs.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. Yet diffusion models that directly work on discrete data space do not fully exploit the power of iterative refinement, as the signals are lost during the transition between discrete states. Existing continuous diffusion models for discrete data have limited performance compared to discrete approaches, and the unclear link between them restricts the development of diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on the analogy, we introduce a simple design for the diffusion process that generalizes previous discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry and a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. Codes available at https://github.com/harryjo97/RDLM{https://github.com/harryjo97/RDLM}.

Diffusion Language Models (DLMs) are rapidly emerging as a powerful and promising alternative to the dominant autoregressive (AR) paradigm. By generating tokens in parallel through an iterative denoising process, DLMs possess inherent advantages in reducing inference latency and capturing bidirectional context, thereby enabling fine-grained control over the generation process. While achieving a several-fold speed-up, recent advancements have allowed DLMs to show performance comparable to their autoregressive counterparts, making them a compelling choice for various natural language processing tasks. In this survey, we provide a holistic overview of the current DLM landscape. We trace its evolution and relationship with other paradigms, such as autoregressive and masked language models, and cover both foundational principles and state-of-the-art models. Our work offers an up-to-date, comprehensive taxonomy and an in-depth analysis of current techniques, from pre-training strategies to advanced post-training methods. Another contribution of this survey is a thorough review of DLM inference strategies and optimizations, including improvements in decoding parallelism, caching mechanisms, and generation quality. We also highlight the latest approaches to multimodal extensions of DLMs and delineate their applications across various practical scenarios. Furthermore, our discussion addresses the limitations and challenges of DLMs, including efficiency, long-sequence handling, and infrastructure requirements, while outlining future research directions to sustain progress in this rapidly evolving field. Project GitHub is available at https://github.com/VILA-Lab/Awesome-DLMs.

Masked diffusion language models (dLMs) generate text through bidirectional denoising, yet this capability remains locked for infilling prompts. This limitation is an artifact of the current supervised finetuning (SFT) convention of applying response-only masking. To unlock this capability, we extend full-sequence masking during SFT, where both prompts and responses are masked jointly. Once unlocked, the model infills masked portions of a prompt template conditioned on few-shot examples. We show that such model-infilled prompts match or surpass manually designed templates, transfer effectively across models, and are complementary to existing prompt optimization methods. Our results suggest that training practices, not architectural limitations, are the primary bottleneck preventing masked diffusion language models from infilling effective prompts

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.

The recent surge of generative AI has been fueled by the generative power of diffusion probabilistic models and the scalable capabilities of large language models. Despite their potential, it remains elusive whether diffusion language models can solve general language tasks comparable to their autoregressive counterparts. This paper demonstrates that scaling diffusion models w.r.t. data, sizes, and tasks can effectively make them strong language learners. We build competent diffusion language models at scale by first acquiring knowledge from massive data via masked language modeling pretraining thanks to their intrinsic connections. We then reprogram pretrained masked language models into diffusion language models via diffusive adaptation, wherein task-specific finetuning and instruction finetuning are explored to unlock their versatility in solving general language tasks. Experiments show that scaling diffusion language models consistently improves performance across downstream language tasks. We further discover that instruction finetuning can elicit zero-shot and few-shot in-context learning abilities that help tackle many unseen tasks by following natural language instructions, and show promise in advanced and challenging abilities such as reasoning.

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.

In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output controllability, and dynamic, response-aware perception. These capabilities are previously difficult to achieve with AR models. Recently, a growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10x acceleration in inference speed. The advancement of discrete diffusion LLMs and MLLMs has been largely driven by progress in two domains. The first is the development of autoregressive LLMs and MLLMs, which has accumulated vast amounts of data, benchmarks, and foundational infrastructure for training and inference. The second contributing domain is the evolution of the mathematical models underlying discrete diffusion. Together, these advancements have catalyzed a surge in dLLMs and dMLLMs research in early 2025. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, and categorize representative models. We further analyze key techniques for training and inference, and summarize emerging applications across language, vision-language, and biological domains. We conclude by discussing future directions for research and deployment. Paper collection: https://github.com/LiQiiiii/DLLM-Survey

Recent advances in masked diffusion language models (MDLMs) narrow the quality gap to autoregressive LMs, but their sampling remains expensive because generation requires many full-sequence denoising passes with a large Transformer and, unlike autoregressive decoding, cannot benefit from KV caching. In this work, we exploit the flexibility of the diffusion framework and study model scheduling, where a smaller MDLM replaces the full model at a subset of denoising steps. Across models trained on OpenWebText and LM1B, we show that early and late denoising steps are substantially more robust to such replacement than middle steps, enabling up to a 17% reduction in FLOPs with only modest degradation in generative perplexity under both unconditional and prefix-conditional generation, while preserving sample diversity. We support these findings with a step-importance analysis based on loss and KL divergence between small and large models across timesteps, as well as an exhaustive search over coarse step segments, both of which identify the middle of the diffusion trajectory as most sensitive consistently across datasets. Our results suggest that simple, architecture-agnostic scheduling rules can significantly accelerate MDLM sampling while largely preserving generation quality.

Diffusion and flow-based models have become the de facto approaches for generating continuous data, e.g., in domains such as images and videos. Their success has attracted growing interest in applying them to language modeling. Unlike their image-domain counterparts, today's leading diffusion language models (DLMs) primarily operate over discrete tokens. In this paper, we show that continuous DLMs can be made effective with minimal adaptation to the discrete domain. We propose Embedded Language Flows (ELF), a class of diffusion models in continuous embedding space based on continuous-time Flow Matching. Unlike existing DLMs, ELF predominantly stays within the continuous embedding space until the final time step, where it maps to discrete tokens using a shared-weight network. This formulation makes it straightforward to adapt established techniques from image-domain diffusion models, e.g., classifier-free guidance (CFG). Experiments show that ELF substantially outperforms leading discrete and continuous DLMs, achieving better generation quality with fewer sampling steps. These results suggest that ELF offers a promising path toward effective continuous DLMs.

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 (with 127M, 355M, and 7B parameters) 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.

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.

We introduce LLaDA-MoE, a large language diffusion model with the Mixture-of-Experts (MoE) architecture, trained from scratch on approximately 20T tokens. LLaDA-MoE achieves competitive performance with significantly reduced computational overhead by maintaining a 7B-parameter capacity while activating only 1.4B parameters during inference. Our empirical evaluation reveals that LLaDA-MoE achieves state-of-the-art performance among diffusion language models with larger parameters, surpassing previous diffusion language models LLaDA, LLaDA 1.5, and Dream across multiple benchmarks. The instruct-tuned model LLaDA-MoE-7B-A1B-Instruct demonstrates capabilities comparable to Qwen2.5-3B-Instruct in knowledge understanding, code generation, mathematical reasoning, agent and alignment tasks, despite using fewer active parameters. Our results show that integrating a sparse MoE architecture into the training objective of masked diffusion language models still brings out MoE's strengths under efficient inference with few active parameters, and opens ample room for further exploration of diffusion language models. LLaDA-MoE models are available at Huggingface.

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 1.3times sampling speedup over existing diffusion models.

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.

In autoregressive language models, each token is sampled by conditioning on all the past tokens; the overall string has thus been sampled from the correct underlying joint distribution represented by the model. In contrast, masked diffusion language models generate text by unmasking tokens out of order and potentially in parallel. Generating an overall string sampled from the correct underlying joint distribution would (again) require exactly one token unmasking in every full-model forward pass. The more tokens unmasked in parallel, the further away the string is from the true joint; this can be seen in the resulting drop in accuracy (but, increase in speed). In this paper we devise a way to {\em approximately} sample multiple tokens from the joint distribution in a single full-model forward pass; we do so by developing a new lightweight single-layer ``sampler" on top of an existing large diffusion LM. One forward pass of the full model can now be followed by multiple forward passes of only this sampler layer, to yield multiple unmasked tokens. Our sampler is trained to mimic exact joint sampling from the (frozen) full model. We show the effectiveness of our approximate joint sampling for both pretrained-only (Dream-7B-Base) and instruction-tuned (Dream-7B-Instruct) models on language modeling and math \& coding tasks. When four tokens are unmasked for each full-model denoising step, our sampling algorithm achieves a MAUVE score of 0.87 (vs marginal baseline of 0.31) with respect to the true joint distribution.

Autoregressive (AR) models have long dominated the landscape of large language models, driving progress across a wide range of tasks. Recently, diffusion-based language models have emerged as a promising alternative, though their advantages over AR models remain underexplored. In this paper, we systematically study masked diffusion models in data-constrained settings-where training involves repeated passes over limited data-and find that they significantly outperform AR models when compute is abundant but data is scarce. Diffusion models make better use of repeated data, achieving lower validation loss and superior downstream performance. We interpret this advantage as implicit data augmentation: masked diffusion exposes the model to a diverse distribution of token orderings and prediction tasks, unlike AR's fixed left-to-right factorization. We find new scaling laws for diffusion models and derive a closed-form expression for the critical compute threshold at which diffusion begins to outperform AR. These results suggest that when data, not compute, is the bottleneck, diffusion models offer a compelling alternative to the standard AR paradigm. Our code is available at: https://diffusion-scaling.github.io.

Large Language Models (LLMs) have revolutionized language modeling through autoregressive generation, enabling strong performance across a wide range of tasks. Recently, Diffusion Language Models (DLMs) have emerged as an alternative paradigm that generates text through iterative denoising rather than next-token prediction, allowing parallel refinement of entire sequences. While numerous diffusion-based architectures have been proposed, differences in evaluation protocols, datasets, inference budgets, and generation hyperparameters make it difficult to compare their capabilities and understand the trade-offs they offer. In this work, we present a systematic experimental analysis of modern DLMs. Specifically, we evaluate eight state-of-the-art DLMs across eight benchmarks spanning reasoning, coding, translation, knowledge, and structured problem solving, while explicitly considering both generation quality and computational efficiency. Beyond downstream evaluation, we analyze the impact of key inference-time factors, including denoising steps, context length, block size, and parallel unmasking strategies, and complement large-scale experiments with controlled comparisons of smaller models trained under identical conditions. Our analysis highlights the strengths and limitations of diffusion-based language modeling across different tasks, architectures, and inference budgets. We show that the behavior of DLMs is strongly influenced by generation-time design choices, leading to distinct trade-offs between performance and computational efficiency. Overall, our study provides practical insights into the capabilities and deployment characteristics of contemporary DLMs.

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) generation, yet their reliance on Transformer backbones limits inference efficiency due to quadratic attention or KV-cache overhead. We introduce DiffuMamba, a masked diffusion language model built on a bidirectional Mamba backbone that combines the diffusion objective with linear-time sequence modeling, and DiffuMamba-H, a hybrid variant with interleaved attention. Across scales up to 1.3B parameters, our models match Transformer-based diffusion in downstream performance while achieving up to 8.2x and 4.3x higher inference throughput, respectively, on long sequences. We further present a systematic analysis of inference efficiency across modern DLM variants combining asymptotic complexity with empirical measurements. Notably, cache-efficient block diffusion with Mamba mixers emerges as the only strategy that scales linearly with sequence length and achieves the strongest performance across all baselines, suggesting a promising direction for future diffusion-based generation systems.

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.

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as is standard in language modeling. We propose Self-conditioned Embedding Diffusion, a continuous diffusion mechanism that operates on token embeddings and allows to learn flexible and scalable diffusion models for both conditional and unconditional text generation. Through qualitative and quantitative evaluation, we show that our text diffusion models generate samples comparable with those produced by standard autoregressive language models - while being in theory more efficient on accelerator hardware at inference time. Our work paves the way for scaling up diffusion models for text, similarly to autoregressive models, and for improving performance with recent refinements to continuous diffusion.

Standard discrete diffusion models treat all unobserved states identically by mapping them to an absorbing [MASK] token. This creates an 'information void' where semantic information that could be inferred from unmasked tokens is lost between denoising steps. We introduce Continuously Augmented Discrete Diffusion (CADD), a framework that augments the discrete state space with a paired diffusion in a continuous latent space. This yields graded, gradually corrupted states in which masked tokens are represented by noisy yet informative latent vectors rather than collapsed 'information voids'. At each reverse step, CADD may leverage the continuous latent as a semantic hint to guide discrete denoising. The design is clean and compatible with existing discrete diffusion training. At sampling time, the strength and choice of estimator for the continuous latent vector enables a controlled trade-off between mode-coverage (generating diverse outputs) and mode-seeking (generating contextually precise outputs) behaviors. Empirically, we demonstrate CADD improves generative quality over mask-based diffusion across text generation, image synthesis, and code modeling, with consistent gains on both qualitative and quantitative metrics against strong discrete baselines.

Diffusion language models (DLMs) generate text through iterative denoising, but inference requires full-sequence attention at every iteration, resulting in substantial redundant computation on masked tokens. Block-wise diffusion can reduce this cost, yet it typically relies on retraining and constrained update orders, limiting its direct applicability to pretrained DLMs. Our token-level analysis reveals pronounced structural locality in DLM inference. Decoding is driven by a small set of prefix-localized active tokens; the influence of distant undecoded context diminishes rapidly, and decoded tokens exhibit stage-wise temporal stability, enabling reuse of intermediate representations except for a brief post-decode transient. Motivated by these observations, we propose \placeholderThe source code is available at https://github.com/vhicrgit/Window-Diffusion., a window-based token pruning and caching method for inference. We maintain a local computation window that slides rightward as denoising progresses, and partition undecoded tokens into: (i) active tokens that are computed online, (ii) buffer tokens whose KV states are cached and periodically refreshed, and (iii) far-field tokens that are pruned outside the window. Computation is restricted to active and buffer tokens within the window, while far-field tokens are omitted at each stage. Experiments on LLaDA and Dream show that, under matched compute budgets, our method achieves up to 99times inference speedup while largely preserving generation performance.

Despite the growing success of diffusion models in continuous-valued domains (e.g., images), similar efforts for discrete domains such as text have yet to match the performance of autoregressive language models. In this work, we present SSD-LM -- a diffusion-based language model with two key design choices. First, SSD-LM is semi-autoregressive, iteratively generating blocks of text, allowing for flexible output length at decoding time while enabling local bidirectional context updates. Second, it is simplex-based, performing diffusion on the natural vocabulary space rather than a learned latent space, allowing us to incorporate classifier guidance and modular control using off-the-shelf classifiers without any adaptation. We evaluate SSD-LM on unconstrained text generation benchmarks, and show that it matches or outperforms strong autoregressive GPT-2 models across standard quality and diversity metrics, while vastly outperforming diffusion-based baselines. On controlled text generation, SSD-LM also outperforms competitive baselines, with an extra advantage in modularity.

While diffusion has drawn considerable recent attention from the language modeling community, continuous diffusion has appeared less scalable than discrete approaches. To challenge this belief we revisit Plaid, a likelihood-based continuous diffusion language model (DLM), and construct RePlaid by aligning the architecture of Plaid with modern discrete DLMs. In this unified setting, we establish the first scaling law for continuous DLMs that rivals discrete DLMs: RePlaid exhibits a compute gap of only 20times compared to autoregressive models, outperforms Duo while using fewer parameters, and outperforms MDLM in the over-trained regime. We benchmark RePlaid against recent continuous DLMs: on OpenWebText, RePlaid achieves a new state-of-the-art PPL bound of 22.1 among continuous DLMs and superior generation quality. These results suggest that continuous diffusion, when trained via likelihood, is a highly competitive and scalable alternative to discrete DLMs. Moreover, we offer theoretical insights to understand the advantage of likelihood-based training. We show that optimizing the noise schedule to minimize the ELBO's variance naturally yields linear cross-entropy (information loss) over time. This evenly distributes denoising difficulty without any case-specific time reparameterization. In addition, we find that optimizing embeddings via likelihood creates structured geometries and drives the most significant likelihood gain.

Masked Diffusion Language Models (MDLMs) have emerged as a distinct paradigm for sequence generation. As MDLMs become diverse in capabilities and knowledge coverage, an important question is how to combine their knowledge. Toward this, we first investigate the unique decoding dynamics of MDLMs. We find that successful generations exhibit stable confidence dynamics over answer-relevant positions, while unreliable trajectories can often be corrected by injecting promising intermediate states from other models. Guided by this observation, we propose TIE (Trajectory-based Iterative Ensembling), a knowledge fusion framework in which MDLMs iteratively identify reliable decoding trajectories and relay them across models. TIE tracks confidence dynamics over answer-relevant positions to determine which model currently follows a more reliable trajectory and selectively transfers partially denoised sequences across models. As the model on the more promising trajectory often changes across denoising steps, TIE allows different models to contribute complementary strengths at different stages of generation. Strong performance across diverse reasoning tasks, along with our analyses, suggests that TIE offers a practical approach to the underexplored problem of MDLM ensembling.

Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have presented diffusion as an alternative to autoregressive language generation. We instead view diffusion as a complementary method that can augment the generative capabilities of existing pre-trained language models. We demonstrate that continuous diffusion models can be learned in the latent space of a pre-trained encoder-decoder model, enabling us to sample continuous latent representations that can be decoded into natural language with the pre-trained decoder. We show that our latent diffusion models are more effective at sampling novel text from data distributions than a strong autoregressive baseline and also enable controllable generation.

Diffusion language models have emerged as a promising approach for text generation. One would naturally expect this method to be an efficient replacement for autoregressive models since multiple tokens can be sampled in parallel during each diffusion step. However, its efficiency-accuracy trade-off is not yet well understood. In this paper, we present a rigorous theoretical analysis of a widely used type of diffusion language model, the Masked Diffusion Model (MDM), and find that its effectiveness heavily depends on the target evaluation metric. Under mild conditions, we prove that when using perplexity as the metric, MDMs can achieve near-optimal perplexity in sampling steps regardless of sequence length, demonstrating that efficiency can be achieved without sacrificing performance. However, when using the sequence error rate--which is important for understanding the "correctness" of a sequence, such as a reasoning chain--we show that the required sampling steps must scale linearly with sequence length to obtain "correct" sequences, thereby eliminating MDM's efficiency advantage over autoregressive models. Our analysis establishes the first theoretical foundation for understanding the benefits and limitations of MDMs. All theoretical findings are supported by empirical studies.

Diffusion language models (DLMs) have shown strong potential for general natural language tasks with in-context examples. However, due to the bidirectional attention mechanism, DLMs incur substantial computational cost as context length increases. This work addresses this issue with a key discovery: unlike the sequential generation in autoregressive language models (ARLMs), the diffusion generation paradigm in DLMs allows efficient dynamic adjustment of the context during generation. Building on this insight, we propose Dynamic In-Context Planner (DIP), a context-optimization method that dynamically selects and inserts in-context examples during generation, rather than providing all examples in the prompt upfront. Results show DIP maintains generation quality while achieving up to 12.9times inference speedup over standard inference and 1.17times over KV cache-enhanced inference.

We introduce ``Partition Generative Models'' (PGMs), a novel approach to masked generative modeling (MGMs), particularly effective for masked diffusion language modeling (MDLMs). PGM divides tokens into two distinct groups and employs sparse attention patterns to prevent cross-group information exchange. Hence, the model is trained to predict tokens in one group based solely on information from the other group. This partitioning strategy eliminates the need for MASK tokens entirely. While traditional MGMs inefficiently process MASK tokens during generation, PGMs achieve greater computational efficiency by operating exclusively on unmasked tokens. Our experiments on OpenWebText with a context length of 1024 tokens demonstrate that PGMs deliver at least 5x improvements in both latency and throughput compared to MDLM when using the same number of sampling steps, while generating samples with better generative perplexity than MDLM. Finally, we show that PGMs can be distilled with Self-Distillation Through Time (SDTT), a method originally devised for MDLM, in order to achieve further inference gains.

Diffusion Language Models (DLMs) have recently achieved strong results in text generation. However, their multi-step sampling leads to slow inference, limiting practical use. To address this, we extend Inverse Distillation, a technique originally developed to accelerate continuous diffusion models, to the discrete setting. Nonetheless, this extension introduces both theoretical and practical challenges. From a theoretical perspective, the inverse distillation objective lacks uniqueness guarantees, which may lead to suboptimal solutions. From a practical standpoint, backpropagation in the discrete space is non-trivial and often unstable. To overcome these challenges, we first provide a theoretical result demonstrating that our inverse formulation admits a unique solution, thereby ensuring valid optimization. We then introduce gradient-stable relaxations to support effective training. As a result, experiments on multiple DLMs show that our method, Inverse-distilled Diffusion Language Models (IDLM), reduces the number of inference steps by 4x-64x, while preserving the teacher model's entropy and generative perplexity.

Language models based on discrete diffusion have attracted widespread interest for their potential to provide faster generation than autoregressive models. In practice, however, they exhibit a sharp degradation of sample quality in the few-step regime, failing to realize this promise. Here we show that language models leveraging flow-based continuous denoising can outperform discrete diffusion in both quality and speed. By revisiting the fundamentals of flows over discrete modalities, we build a flow-based language model (FLM) that performs Euclidean denoising over one-hot token encodings. We show that the model can be trained by predicting the clean data via a cross entropy objective, where we introduce a simple time reparameterization that greatly improves training stability and generation quality. By distilling FLM into its associated flow map, we obtain a distilled flow map language model (FMLM) capable of few-step generation. On the LM1B and OWT language datasets, FLM attains generation quality matching state-of-the-art discrete diffusion models. With FMLM, our approach outperforms recent few-step language models across the board, with one-step generation exceeding their 8-step quality. Our work calls into question the widely held hypothesis that discrete diffusion processes are necessary for generative modeling over discrete modalities, and paves the way toward accelerated flow-based language modeling at scale. Code is available at https://github.com/david3684/flm.

We present DMax, a new paradigm for efficient diffusion language models (dLLMs). It mitigates error accumulation in parallel decoding, enabling aggressive decoding parallelism while preserving generation quality. Unlike conventional masked dLLMs that decode through a binary mask-to-token transition, DMax reformulates decoding as a progressive self-refinement from mask embeddings to token embeddings. At the core of our approach is On-Policy Uniform Training, a novel training strategy that efficiently unifies masked and uniform dLLMs, equipping the model to recover clean tokens from both masked inputs and its own erroneous predictions. Building on this foundation, we further propose Soft Parallel Decoding. We represent each intermediate decoding state as an interpolation between the predicted token embedding and the mask embedding, enabling iterative self-revising in embedding space. Extensive experiments across a variety of benchmarks demonstrate the effectiveness of DMax. Compared with the original LLaDA-2.0-mini, our method improves TPF on GSM8K from 2.04 to 5.47 while preserving accuracy. On MBPP, it increases TPF from 2.71 to 5.86 while maintaining comparable performance. On two H200 GPUs, our model achieves an average of 1,338 TPS at batch size 1. Code is available at: https://github.com/czg1225/DMax

Diffusion Language Models (DLMs) have recently emerged as a promising alternative to autoregressive models. Unlike standard diffusion-based approaches, DLMs are not explicitly conditioned on a timestep, raising a natural question: do these models internally represent denoising progress, and how is such information used downstream? In this work, we show that DLMs do in fact encode a latent representation related to the diffusion timestep within their residual streams. We find that this signal can be reliably extracted using probes across layers, indicating that denoising progress is decodable from internal activations. We further demonstrate that steering the model along a low-dimensional subspace associated with the inferred timestep allows us to systematically modulate its notion of denoising progress, leading to predictable changes in model confidence and entropy. Finally, we analyse the geometry of the identified representation, showing that it exhibits structured and interpretable properties in activation space, and shedding light on how such a signal is processed by these models.

Diffusion models have emerged as a powerful paradigm for modern generative modeling, demonstrating strong potential for large language models (LLMs). Unlike conventional autoregressive (AR) models that generate tokens sequentially, diffusion models enable parallel token sampling, leading to faster generation and eliminating left-to-right generation constraints. Despite their empirical success, the theoretical understanding of diffusion model approaches remains underdeveloped. In this work, we develop convergence guarantees for diffusion language models from an information-theoretic perspective. Our analysis demonstrates that the sampling error, measured by the Kullback-Leibler (KL) divergence, decays inversely with the number of iterations T and scales linearly with the mutual information between tokens in the target text sequence. In particular, we establish matching upper and lower bounds, up to some constant factor, to demonstrate the tightness of our convergence analysis. These results offer novel theoretical insights into the practical effectiveness of diffusion language models.

Continuous diffusion has been the foundation of high-fidelity, controllable, and few-step generation of many data modalities such as images. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind discrete counterparts due to the sparse data space and the underexplored design space. In this work, we close this gap with LangFlow, the first continuous DLM to rival discrete diffusion, by connecting embedding-space DLMs to Flow Matching via Bregman divergence, alongside three key innovations: (1) we derive a novel ODE-based NLL bound for principled evaluation of continuous flow-based language models; (2) we propose an information-uniform principle for setting the noise schedule, which motivates a learnable noise scheduler based on a Gumbel distribution; and (3) we revise prior training protocols by incorporating self-conditioning, as we find it improves both likelihood and sample quality of embedding-space DLMs with effects substantially different from discrete diffusion. Putting everything together, LangFlow rivals top discrete DLMs on both the perplexity (PPL) and the generative perplexity (Gen. PPL), reaching a PPL of 30.0 on LM1B and 24.6 on OpenWebText. It even exceeds autoregressive baselines in zero-shot transfer on 4 out of 7 benchmarks. LangFlow provides the first clear evidence that continuous diffusion is a promising paradigm for language modeling. Homepage: https://github.com/nealchen2003/LangFlow

Modern large language models are predominantly trained with autoregressive factorization and causal attention. We present iLLaDA, an 8B masked diffusion language model trained from scratch with fully bidirectional attention. iLLaDA keeps the masked diffusion objective throughout pre-training and supervised fine-tuning (SFT), scaling pre-training to 12T tokens and fine-tuning on a 25B-token instruction corpus for 12 epochs. We further use variable-length generation for efficiency and introduce confidence-based scoring for multiple-choice evaluation. Compared with LLaDA, iLLaDA improves broadly across general, mathematical, and code benchmarks; for example, iLLaDA-Base improves by 21.6 points on BBH and 14.9 points on ARC-Challenge, while iLLaDA-Instruct improves by 14.5 points on MATH and 16.5 points on HumanEval. Despite its non-autoregressive training, iLLaDA also remains competitive with Qwen2.5 7B on several benchmarks. These results show that fully bidirectional diffusion training from scratch is a competitive path toward strong language models. Model weights and codes: https://github.com/ML-GSAI/LLaDA.

Recent studies have shown that diffusion language models achieve remarkable data efficiency under limited-data constraints, yet the underlying mechanisms remain unclear. In this work, we perform extensive ablation experiments to disentangle the sources of this efficiency. Our results show that random masking of input tokens plays the dominant role. We further show that similar gains can be obtained through in MLP dropout and weight decay, indicating that stochastic regularization broadly enhances data efficiency in multi-epoch training. Our code is available at https://github.com/zitian-gao/data-efficiency.

This paper combines autoregressive and masked-diffusion training objectives without any architectural modifications, resulting in flexible language models that outperform single-objective models. Autoregressive modeling has been a popular approach, partly because of its training efficiency; however, that comes at the cost of sensitivity to overfitting. On the other hand, masked-diffusion models are less efficient to train while being more resilient to overfitting. In this work, we demonstrate that dual-objective training achieves the best of both worlds. To derive the optimal balance between both objectives, we train and evaluate 50 language models under varying levels of data repetition. We show that it is optimal to combine both objectives under all evaluated settings and that the optimal balance is similar whether targeting autoregressive or masked-diffusion downstream performance.

Diffusion language models (DLMs) have recently demonstrated capabilities that complement standard autoregressive (AR) models, particularly in non-sequential generation and bidirectional editing. Although recent work has shown that pretrained autoregressive checkpoints can be converted into diffusion language models, existing recipes primarily transfer parameters through continued denoising training with objective- and attention-level modifications. We instead ask whether the internal representation geometry learned by next-token prediction can be explicitly preserved during AR-to-DLM conversion. We hypothesize that much of the semantic structure learned by AR pretraining can transfer across generation orders, and thus DLM training should be viewed as relearning the decoding path rather than relearning language representations. To investigate this, we introduce REPR-ALIGN, a representation alignment objective that adapts a bidirectional masked diffusion model to reuse representations from a pretrained AR model of identical architecture. Concretely, we align the hidden states of the DLM to the frozen AR model at every layer using cosine similarity, while optimizing the standard masked denoising objective. This simple alignment, with no adapters and no architectural changes beyond the attention mask, yields up to 4x training acceleration in our setting and is particularly effective in low-data regimes. Our results suggest that linguistic representations can transfer across generation order, and that representation alignment provides a simple and effective technique for training diffusion language models. Code is available at https://github.com/pengzhangzhi/Open-dLLM.

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.

Diffusion language models offer parallel token generation and inherent bidirectionality, promising more efficient and powerful sequence modeling compared to autoregressive approaches. However, state-of-the-art diffusion models (e.g., Dream 7B, LLaDA 8B) suffer from slow inference. While they match the quality of similarly sized Autoregressive (AR) Models (e.g., Qwen2.5 7B, Llama3 8B), their iterative denoising requires multiple full-sequence forward passes, resulting in high computational costs and latency, particularly for long input prompts and long-context scenarios. Furthermore, parallel token generation introduces token incoherence problems, and current sampling heuristics suffer from significant quality drops with decreasing denoising steps. We address these limitations with two training-free techniques. First, we propose FreeCache, a Key-Value (KV) approximation caching technique that reuses stable KV projections across denoising steps, effectively reducing the computational cost of DLM inference. Second, we introduce Guided Diffusion, a training-free method that uses a lightweight pretrained autoregressive model to supervise token unmasking, dramatically reducing the total number of denoising iterations without sacrificing quality. We conduct extensive evaluations on open-source reasoning benchmarks, and our combined methods deliver up to a 34x end-to-end speedup without compromising accuracy. For the first time, diffusion language models achieve a comparable and even faster latency as the widely adopted autoregressive models. Our work successfully paved the way for scaling up the diffusion language model to a broader scope of applications across different domains.

We introduce DiffusionGemma, an experimental open-weight language model that uses discrete diffusion to generate text at exceptionally high speed. Rather than decoding one token at a time, DiffusionGemma iteratively refines blocks of 256 tokens in parallel, avoiding the sequential decoding bottleneck of conventional autoregressive (AR) large language models. Instead of training from scratch, we obtain DiffusionGemma by fine-tuning the mixture-of-experts Gemma 4 model with 3.8B activated and 25.2B total parameters. Our compute-efficient two-stage training pipeline uses fewer than 10% of the starting AR model's total training token budget. The first stage uses supervised fine-tuning to teach bidirectional denoising, while the second stage combines reinforcement learning with sampler distillation to jointly improve generation quality and inference efficiency. DiffusionGemma establishes a new Pareto frontier for the trade-off between generation speed and model capability. Averaged across our full evaluation suite, it generates around 20 tokens per forward pass and achieves roughly 1,500 output tokens per second on a single NVIDIA H100 GPU, which is substantially faster than AR models even with state-of-the-art speculative decoding. DiffusionGemma also retains the starting model's support for thinking mode, multimodal inputs, and long contexts. Despite diffusion fine-tuning, it remains capable of AR generation with only minor performance degradation, suggesting a path toward hybrid diffusion-AR decoding.

Diffusion Large Language Models (DLLMs) enable fully parallel token decoding but often remain impractical at inference time due to the many denoising iterations required to refine an information-free, fully masked initialization into coherent text. Most existing acceleration methods focus on traversing this generative trajectory more efficiently via improved solvers or sampling strategies. We advance a complementary perspective: shorten the trajectory itself by starting closer to the target distribution through context-aware initialization. We propose a training-free interface that injects prompt-conditioned priors from a lightweight auxiliary model into the diffusion initialization, and instantiate it with two mechanisms: discrete token injection and representation-level embedding interpolation. Because injected priors can be imperfect and unmask-only decoding can over-commit early, we also introduce a simple confidence-based remasking mechanism as a form of prior skepticism. Preliminary evidence on GSM8K suggests that context-aware initialization can substantially reduce denoising iterations (about 35\% fewer function evaluations in our setting), while also exposing a key open challenge: naive warm-starting can degrade final accuracy relative to strong diffusion baselines. We use these findings to motivate a research agenda around calibration, revision mechanisms, and representation alignment for reliable warm-started diffusion decoding.

Diffusion language models (DLMs) have recently emerged as a promising alternative to autoregressive models, primarily due to their ability to enable parallel decoding. Despite this advantage, most existing DLMs rely on a fixed generation length specified prior to decoding, which restricts their flexibility in real-world applications. While a few recent works attempt to support flexible-length generation, they typically suffer from notable limitations: some require costly retraining to accommodate variable-length outputs, while others depend solely on local confidence signals during decoding. Such local criteria fail to capture the evolving structure of the sequence, often resulting in suboptimal generation quality. In this paper, we propose a training-free, Bayesian structured decoding framework that formulates flexible-length generation as a dynamic structural inference problem. Our approach formulates flexible-length generation as a dynamic structural inference problem, jointly computing the expansion length, the block boundaries, and the decoding schedule. At each window expansion step, the method integrates local uncertainty with structural signals via a unified mechanism that supports dynamic structured generation, including both flexible block expansion and block organization, while maintaining coherence. Extensive experiments across multiple benchmarks demonstrate that our approach significantly improves generation quality and flexibility over existing fixed-length and flexible-length baselines. These results highlight the advantage of Bayesian structured decoding for diffusion language model, providing a principled and efficient solution for structured text generation.

We propose a diffusion-based framework for prompt optimization that leverages Diffusion Language Models (DLMs) to iteratively refine system prompts through masked denoising. By conditioning on interaction traces, including user queries, model responses, and optional feedback, our method enables flexible, span-level prompt updates without requiring gradient access or modifying the downstream language model. Across diverse benchmarks (e.g., τ-bench, SST-2, SST-5), DLM-optimized prompts consistently improve the performance of a frozen target LLM (e.g., GPT-4o-mini). We further show that moderate diffusion step counts provide the best balance between refinement quality and stability. These results highlight diffusion-based prompt optimization as a general, model-agnostic, and scalable approach for enhancing LLM performance through iterative prompt refinement.

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion approaches over token embeddings have narrowed this gap, suggesting continuous state spaces are highly effective for language. In this work, we further close the autoregressive gap by modeling text as a continuous diffusion process over fixed-width binary bitstreams. Our approach represents semantic tokens as analog bit sequences and utilizes a matched-filter residual parameterization to isolate contextual learning from analytic independent-bit posteriors. Crucially, we adopt a stochastic sampler that applies Langevin-type corrections gated by the entropy-rate profile, automatically concentrating stochasticity in high-information regions while remaining nearly deterministic elsewhere. On the One Billion Word Benchmark (LM1B), our 130M-parameter bitstream model reaches a generative perplexity (GenPPL) of 59.76 at matched real-data entropy (4.31) using 256 neural function evaluations (NFEs), decisively outperforming prior DLM baselines and reaching the autoregressive reference. On OpenWebText (OWT), our stochastic sampler establishes a new continuous-DLM Pareto frontier, achieving GenPPL=27.06 at an entropy of 5.26 using 4times fewer steps than previous 1024-NFE baselines. As an additional architectural benefit, bitstream diffusion removes the O(V) vocabulary scaling bottleneck shared by standard DLMs. By predicting O(log V) bitwise logits via semantic bit-patching, our model yields a reduced memory footprint and higher throughput, demonstrating a scalable paradigm for language generation as vocabulary sizes grow.

Diverse outputs in text generation are necessary for effective exploration in complex reasoning tasks, such as code generation and mathematical problem solving. Such Pass@k problems benefit from distinct candidates covering the solution space. However, traditional sampling approaches often waste computational resources on repetitive failure modes. While Diffusion Language Models have emerged as a competitive alternative to the prevailing Autoregressive paradigm, they remain susceptible to this redundancy, with independent samples frequently collapsing into similar modes. To address this, we propose a training free, low cost intervention to enhance generative diversity in Diffusion Language Models. Our approach modifies intermediate samples in a batch sequentially, where each sample is repelled from the feature space of previous samples, actively penalising redundancy. Unlike prior methods that require retraining or beam search, our strategy incurs negligible computational overhead, while ensuring that each sample contributes a unique perspective to the batch. We evaluate our method on the HumanEval and GSM8K benchmarks using the LLaDA-8B-Instruct model. Our results demonstrate significantly improved diversity and Pass@k performance across various temperature settings. As a simple modification to the sampling process, our method offers an immediate, low-cost improvement for current and future Diffusion Language Models in tasks that benefit from diverse solution search. We make our code available at https://github.com/sean-lamont/odd.

One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while offering benefits, can cause models to lose this global coherence at the macro level. To regain global contextual understanding while preserving the advantages of the semi-autoregressive paradigm, we propose Diffusion in Diffusion, a 'draft-then-refine' framework designed to overcome the irreversibility and myopia problems inherent in block diffusion models. Our approach first employs block diffusion to generate rapid drafts using small blocks, then refines these drafts through global bidirectional diffusion with a larger bidirectional receptive field. We utilize snapshot confidence remasking to identify the most critical tokens that require modification, and apply mix-scale training to expand the block diffusion model's global capabilities. Empirical results demonstrate that our approach sets a new benchmark for discrete diffusion models on the OpenWebText dataset. Using only 26% of the fine-tuning budget of baseline models, we reduce generative perplexity from 25.7 to 21.9, significantly narrowing the performance gap with autoregressive models.

Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal imbalance, we demonstrate how diffusion models effectively learn difficult subgoals that elude autoregressive approaches. We propose Multi-granularity Diffusion Modeling (MDM), which prioritizes subgoals based on difficulty during learning. On complex tasks like Countdown, Sudoku, and Boolean Satisfiability Problems, MDM significantly outperforms autoregressive models without using search techniques. For instance, MDM achieves 91.5\% and 100\% accuracy on Countdown and Sudoku, respectively, compared to 45.8\% and 20.7\% for autoregressive models. Our work highlights the potential of diffusion-based approaches in advancing AI capabilities for sophisticated language understanding and problem-solving tasks.

Discrete diffusion language models generate text by iteratively denoising an entire response in parallel. At each step, they predict tentative tokens for every masked position, committing the confident predictions to the output and discarding the unconfident ones. We show that the discarded tokens are in fact a useful lookahead signal for retrieval-augmented generation: even low-confidence tokens often surface salient entities early in the denoising trajectory, enabling retrieval of stronger evidence before the output is finalized. We exploit this through Self-Augmenting Retrieval for Diffusion Language Models (SARDI), a dynamic RAG framework that uses these lookahead tokens to guide retrieval during denoising. SARDI is training-free, retriever-agnostic, and applicable to any reasoning-capable discrete diffusion language model. Across five multi-hop QA benchmarks, SARDI outperforms current training-free diffusion and autoregressive retrieval baselines at up to 8times higher throughput.

We propose Nemotron-Labs-Diffusion-Image, a state-of-the-art masked discrete diffusion model (MDM) for high-resolution text-to-image synthesis. Compared with prior work on masked image generation, Nemotron-Labs-Diffusion-Image addresses two key challenges. First, unlike continuous diffusion models which progressively refine latent representations across the entire image, standard MDMs lack self-correcting capability because discrete tokens cannot be modified once they are unmasked. Second, although increasing the vocabulary size of discrete image tokenizers improves reconstruction fidelity, it introduces optimization difficulties for generative modeling as the per-token training signal becomes increasingly sparse. To address the first challenge, Nemotron-Labs-Diffusion-Image incorporates a token-editing mechanism that enables the model to dynamically revise already-unmasked tokens during inference, similar to how a sculptor iteratively refines their work. To tackle the second challenge, we propose a Grouped Cross-Entropy (GCE) objective that assigns positive learning signals to tokens neighboring the ground truth in embedding space, thereby alleviating signal sparsity. To further improve training efficiency, we implement a custom fused operator for GCE that significantly reduces VRAM usage in large-vocabulary settings. Experimental results demonstrate that these innovations substantially improve both training efficiency and image fidelity of masked discrete image generators, achieving a score of 0.90 on GenEval, 86.9 on DPG and 10.76 of HPSv3.

Language remains an outlier in generative modeling: while images, video, and audio are increasingly modeled in continuous latent spaces, text generation still relies predominantly on discrete tokens. Existing continuous language models either inherit embedding spaces not designed for joint generation and decoding, or compress autoencoded latents to ease diffusion, sacrificing token-level fidelity. Instead of simplifying the representation to suit the generative model, we preserve a high-capacity, decodable text latent and design the diffusion model to learn its distribution directly. We introduce AURORA-LM, a continuous-latent diffusion language model that separates the construction of a decodable text representation from the modeling of its distribution. A Query-based Encoder-Decoder organizes text into a high-capacity, prefix-aligned latent sequence, and a Block-causal Diffusion Transformer learns its distribution through flow matching, generating blocks left to right while denoising positions within each block in parallel. Because such a latent is harder for diffusion to model, AURORA-LM restricts only the noisy-input pathway while retaining the full clean-latent prediction target, accommodating full-width latents without reducing decoder-facing capacity. We further calibrate the noise-level distribution to the latent width, and introduce self-trajectory consistency to bridge independently sampled training noise and iterative denoising at inference. AURORA-LM achieves the strongest performance among evaluated continuous and diffusion-based language models on OpenWebText free generation and XSum summarization. Scaling to 1B parameters with about 1500 EFLOPs of total compute yields further gains, surpassing a larger publicly released latent-diffusion language model under a matched evaluation protocol. All experiments are conducted on Ascend NPUs.

Masked diffusion language models (MDLMs) offer the potential for parallel token generation, but most open-source MDLMs decode fewer than 5 tokens per model forward pass even with sophisticated sampling strategies. As a result, their sampling speeds are often comparable to AR + speculative decoding schemes, limiting their advantage over mainstream autoregressive approaches. Existing distillation-based accelerators (dParallel, d3LLM) finetune MDLMs on trajectories generated by a base model, which can become off-policy during finetuning and restrict performance to the quality of the base model's samples. We propose dUltra, an on-policy reinforcement learning framework based on Group Relative Policy Optimization (GRPO) that learns unmasking strategies for efficient parallel decoding. dUltra introduces an unmasking planner head that predicts per-token unmasking likelihoods under independent Bernoulli distributions. We jointly optimize the base diffusion LLM and the unmasking order planner using reward signals combining verifiable reward, distillation reward, and the number of unmasking steps. Across mathematical reasoning and code generation tasks, dUltra improves the accuracy--efficiency trade-off over state-of-the-art heuristic and distillation baselines, moving towards achieving ``diffusion supremacy'' over autoregressive models.

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.

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 models have gained tremendous success in text-to-image generation, yet still lag behind with visual understanding tasks, an area dominated by autoregressive vision-language models. We propose a large-scale and fully end-to-end diffusion model for multi-modal understanding and generation that significantly improves on existing diffusion-based multimodal models, and is the first of its kind to support the full suite of vision-language modeling capabilities. Inspired by the multimodal diffusion transformer (MM-DiT) and recent advances in discrete diffusion language modeling, we leverage a cross-modal maximum likelihood estimation framework that simultaneously trains the conditional likelihoods of both images and text jointly under a single loss function, which is back-propagated through both branches of the diffusion transformer. The resulting model is highly flexible and capable of a wide range of tasks including image generation, captioning, and visual question answering. Our model attained competitive performance compared to recent unified image understanding and generation models, demonstrating the potential of multimodal diffusion modeling as a promising alternative to autoregressive next-token prediction models.

Unlike autoregressive language models, which terminate variable-length generation upon predicting an End-of-Sequence (EoS) token, Diffusion Language Models (DLMs) operate over a fixed maximum-length context window for a predetermined number of denoising steps. However, this process is independent of the required response length, resulting in computational waste for the majority of short responses common in reasoning and chat tasks. To address this problem, we conjecture that the latent prompt representation contains sufficient information to estimate the required output length. We provide empirical evidence for this phenomenon and propose a zero-shot mechanism to dynamically crop the context window before generation begins, leading to fewer diffusion steps and substantial computational savings. We evaluate our approach on four benchmarks with diverse tasks -- GSM8K (reasoning), HumanEval (code generation), IfEval (instruction following), and LongFormQA (question answering) -- revealing massive efficiency gains at minimal performance impact. We report significant reductions in FLOPs across all tasks, with no statistically significant performance degradation, and significant performance improvements in 2 out of 4 tasks.

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 through a 78M parameter model with no access to the target encoder. On 32-token sequences across three embedding models, the method achieves 81.3% token accuracy and 0.87 cosine similarity.

In this paper we introduce token time continuous diffusion (TTCD), a new diffusion language model which (a) operates in continuous space, deterministically mapping Gaussian noise to a final token canvas with no further sampling, and crucially (b) incorporates a new notion of per-token times, with some tokens proceeding from noise to token at a faster rate than others. Continuous space modeling helps TTCD avoid the parallel sampling of multiple tokens, which is a key source of inaccuracy at high speedups for models that iterate purely in discrete space. The notion of per-token times helps TTCD to better model conditional generation, allows for more sure tokens to proceed at a faster rate, and allows for differentiated inter-token influences during refinement. TTCD outperforms discrete models at high speedups. We train a 160M parameter TTCD model on OpenWebText, and then self-distill it; we find that at high speedups we are comparable in unconditional generation quality, and outperform in conditional generation, several existing models of similar size trained, on the same data, and self-distilled. We achieve similar gains in Sudoku solving as well.

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises when important tokens (e.g., key words or low-frequency words that anchor a sentence) are masked early in the forward process, limiting contextual information for accurate reconstruction. To address this, we introduce the Anchored Diffusion Language Model (ADLM), a novel two-stage framework that first predicts distributions over important tokens via an anchor network, and then predicts the likelihoods of missing tokens conditioned on the anchored predictions. ADLM significantly improves test perplexity on LM1B and OpenWebText, achieving up to 25.4% gains over prior DLMs, and narrows the gap with strong AR baselines. It also achieves state-of-the-art performance in zero-shot generalization across seven benchmarks and surpasses AR models in MAUVE score, which marks the first time a DLM generates better human-like text than an AR model. Theoretically, we derive an Anchored Negative Evidence Lower Bound (ANELBO) objective and show that anchoring improves sample complexity and likelihood modeling. Beyond diffusion, anchoring boosts performance in AR models and enhances reasoning in math and logic tasks, outperforming existing chain-of-thought approaches

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 https://github.com/Shark-NLP/DiffuSeq

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Automatic speech recognition is dominated by autoregressive decoders that emit one token at a time. We ask whether a discrete diffusion language model can transcribe speech instead, refining a whole transcript in parallel over a small number of denoising steps. We train an audio-native interface for DiffusionGemma, a 26B mixture-of-experts model that generates text by uniform, random-token discrete diffusion rather than the absorbing-mask scheme common to recent diffusion language models. A frozen Whisper encoder supplies acoustic features, a lightweight projector maps them into the model embedding space, and low-rank adapters let the frozen backbone attend to the new modality. About 42M parameters are trained, which is 0.16 percent of the backbone. We find that the natural training objectives fail to ground the audio because their gradient reaches the projector only through attention that has already dismissed it. A connectionist temporal classification loss applied through the frozen output head breaks this deadlock. The resulting model reaches 6.6 percent word error rate on LibriSpeech test-clean, transcribes in roughly eight parallel steps regardless of utterance length, and uses a single adapter trained on six languages, which we evaluate here on English, Hindi, and Mandarin.

Autoregressive (AR) Large Language Models (LLMs) have demonstrated significant success across numerous tasks. However, the AR modeling paradigm presents certain limitations; for instance, contemporary autoregressive LLMs are trained to generate one token at a time, which can result in noticeable latency. Recent advances have indicated that search and repeated sampling can enhance performance in various applications, such as theorem proving, code generation, and alignment, by utilizing greater computational resources during inference. In this study, we demonstrate that diffusion language models are capable of generating at least 32 tokens simultaneously, while exceeding the performance of AR models in text quality and on the LAMBADA natural language understanding benchmark. This outcome is achieved through a novel distillation method for discrete diffusion models, which reduces the number of inference steps by a factor of 32-64. Practically, our models, even without caching, can generate tokens at a rate that is up to 8 times faster than AR models employing KV caching, and we anticipate further improvements with the inclusion of caching. Moreover, we demonstrate the efficacy of our approach for diffusion language models with up to 860M parameters.

Discrete diffusion models offer global context awareness and flexible parallel generation. However, uniform random noise schedulers in standard DLLM training overlook the highly non-uniform information density inherent in real-world sequences. This wastes optimization resources on low-density structural glues while leaving high-density logical pivot points severely under-optimized. To address this, we propose an Information Density Driven Smart Noise Scheduler. By extracting information-dense hubs and applying Complementary Priority Masking, our method decouples a single training instance into mutually reinforcing reasoning and syntax samples, forcing the model to master both logical deduction and foundational sequence structure. Experiments demonstrate that our approach improves average accuracy by ~4\% across four Code and Math reasoning benchmarks, significantly outperforming uniform baselines. Mechanistic analyses further reveal that probabilistic priority masking effectively mitigates contextual collapse during block diffusion training. Overall, this density-aware strategy efficiently unlocks the reasoning potential of diffusion language models at minimal annotation cost, emerging as a promising new masked data training paradigm for Diffusion LLMs. Our processed dataset can be found at https://huggingface.co/datasets/malr07/opc-sft-stage2-dense-extracted.

Discrete diffusion models enable parallel token sampling for faster inference than autoregressive approaches. However, prior diffusion models use a decoder-only architecture, which requires sampling algorithms that invoke the full network at every denoising step and incur high computational cost. Our key insight is that discrete diffusion models perform two types of computation: 1) representing clean tokens and 2) denoising corrupted tokens, which enables us to use separate modules for each task. We propose an encoder-decoder architecture to accelerate discrete diffusion inference, which relies on an encoder to represent clean tokens and a lightweight decoder to iteratively refine a noised sequence. We also show that this architecture enables faster training of block diffusion models, which partition sequences into blocks for better quality and are commonly used in diffusion language model inference. We introduce a framework for Efficient Encoder-Decoder Diffusion (E2D2), consisting of an architecture with specialized training and sampling algorithms, and we show that E2D2 achieves superior trade-offs between generation quality and inference throughput on summarization, translation, and mathematical reasoning tasks. We provide the code, model weights, and blog post on the project page: https://m-arriola.com/e2d2

Diffusion Language Models (DLMs) have emerged as a compelling alternative to autoregressive approaches, enabling parallel text generation with competitive performance. Despite these advantages, there is a critical instability in DLMs: the moving sink phenomenon. Our analysis indicates that sink tokens exhibit low-norm representations in the Transformer's value space, and that the moving sink phenomenon serves as a protective mechanism in DLMs to prevent excessive information mixing. However, their unpredictable positions across diffusion steps undermine inference robustness. To resolve this, we propose a simple but effective extra sink token implemented via a modified attention mask. Specifically, we introduce a special token constrained to attend solely to itself, while remaining globally visible to all other tokens. Experimental results demonstrate that introducing a single extra token stabilizes attention sinks, substantially improving model performance. Crucially, further analysis confirms that the effectiveness of this token is independent of its position and characterized by negligible semantic content, validating its role as a robust and dedicated structural sink.

Uniform-state discrete diffusion models hold the promise of fast text generation due to their inherent ability to self-correct. However, they are typically outperformed by autoregressive models and masked diffusion models. In this work, we narrow this performance gap by leveraging a key insight: Uniform-state diffusion processes naturally emerge from an underlying Gaussian diffusion. Our method, Duo, transfers powerful techniques from Gaussian diffusion to improve both training and sampling. First, we introduce a curriculum learning strategy guided by the Gaussian process, doubling training speed by reducing variance. Models trained with curriculum learning surpass autoregressive models in zero-shot perplexity on 3 of 7 benchmarks. Second, we present Discrete Consistency Distillation, which adapts consistency distillation from the continuous to the discrete setting. This algorithm unlocks few-step generation in diffusion language models by accelerating sampling by two orders of magnitude. We provide the code and model checkpoints on the project page: http://s-sahoo.github.io/duo

Diffusion models have exhibited remarkable capabilities in text-to-image generation. However, their performance in image-to-text generation, specifically image captioning, has lagged behind Auto-Regressive (AR) models, casting doubt on their applicability for such tasks. In this work, we revisit diffusion models, highlighting their capacity for holistic context modeling and parallel decoding. With these benefits, diffusion models can alleviate the inherent limitations of AR methods, including their slow inference speed, error propagation, and unidirectional constraints. Furthermore, we identify the prior underperformance of diffusion models stemming from the absence of an effective latent space for image-text alignment, and the discrepancy between continuous diffusion processes and discrete textual data. In response, we introduce a novel architecture, LaDiC, which utilizes a split BERT to create a dedicated latent space for captions and integrates a regularization module to manage varying text lengths. Our framework also includes a diffuser for semantic image-to-text conversion and a Back&Refine technique to enhance token interactivity during inference. LaDiC achieves state-of-the-art performance for diffusion-based methods on the MS COCO dataset with 38.2 BLEU@4 and 126.2 CIDEr, demonstrating exceptional performance without pre-training or ancillary modules. This indicates strong competitiveness with AR models, revealing the previously untapped potential of diffusion models in image-to-text generation.

Diffusion Language Models (DLMs) present a compelling alternative to autoregressive models, offering flexible, any-order infilling without specialized prompting design. However, their practical utility is blocked by a critical limitation: the requirement of a fixed-length masked sequence for generation. This constraint severely degrades code infilling performance when the predefined mask size mismatches the ideal completion length. To address this, we propose DreamOn, a novel diffusion framework that enables dynamic, variable-length generation. DreamOn augments the diffusion process with two length control states, allowing the model to autonomously expand or contract the output length based solely on its own predictions. We integrate this mechanism into existing DLMs with minimal modifications to the training objective and no architectural changes. Built upon Dream-Coder-7B and DiffuCoder-7B, DreamOn achieves infilling performance on par with state-of-the-art autoregressive models on HumanEval-Infilling and SantaCoder-FIM and matches oracle performance achieved with ground-truth length. Our work removes a fundamental barrier to the practical deployment of DLMs, significantly advancing their flexibility and applicability for variable-length generation. Our code is available at https://github.com/DreamLM/DreamOn.

Large language models have achieved remarkable success under the autoregressive paradigm, yet high-quality text generation need not be tied to a fixed left-to-right order. Existing alternatives still struggle to jointly achieve generation efficiency, scalable representation learning, and effective global semantic modeling. We propose Cola DLM, a hierarchical latent diffusion language model that frames text generation through hierarchical information decomposition. Cola DLM first learns a stable text-to-latent mapping with a Text VAE, then models a global semantic prior in continuous latent space with a block-causal DiT, and finally generates text through conditional decoding. From a unified Markov-path perspective, its diffusion process performs latent prior transport rather than token-level observation recovery, thereby separating global semantic organization from local textual realization. This design yields a more flexible non-autoregressive inductive bias, supports semantic compression and prior fitting in continuous space, and naturally extends to other continuous modalities. Through experiments spanning 4 research questions, 8 benchmarks, strictly matched ~2B-parameter autoregressive and LLaDA baselines, and scaling curves up to about 2000 EFLOPs, we identify an effective overall configuration of Cola DLM and verify its strong scaling behavior for text generation. Taken together, the results establish hierarchical continuous latent prior modeling as a principled alternative to strictly token-level language modeling, where generation quality and scaling behavior may better reflect model capability than likelihood, while also suggesting a concrete path toward unified modeling across discrete text and continuous modalities.

We present significant extensions to diffusion-based sequence generation models, blurring the line with autoregressive language models. We introduce hyperschedules, which assign distinct noise schedules to individual token positions, generalizing both autoregressive models (e.g., GPT) and conventional diffusion models (e.g., SEDD, MDLM) as special cases. Second, we propose two hybrid token-wise noising processes that interpolate between absorbing and uniform processes, enabling the model to fix past mistakes, and we introduce a novel inference algorithm that leverages this new feature in a simplified context inspired from MDLM. To support efficient training and inference, we design attention masks compatible with KV-caching. Our methods achieve state-of-the-art perplexity and generate diverse, high-quality sequences across standard benchmarks, suggesting a promising path for autoregressive diffusion-based sequence generation.

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

Discrete diffusion is a promising framework for modeling and generating discrete data. In this work, we present Target Concrete Score Matching (TCSM), a novel and versatile objective for training and fine-tuning discrete diffusion models. TCSM provides a general framework with broad applicability. It supports pre-training discrete diffusion models directly from data samples, and many existing discrete diffusion approaches naturally emerge as special cases of our more general TCSM framework. Furthermore, the same TCSM objective extends to post-training of discrete diffusion models, including fine-tuning using reward functions or preference data, and distillation of knowledge from pre-trained autoregressive models. These new capabilities stem from the core idea of TCSM, estimating the concrete score of the target distribution, which resides in the original (clean) data space. This allows seamless integration with reward functions and pre-trained models, which inherently only operate in the clean data space rather than the noisy intermediate spaces of diffusion processes. Our experiments on language modeling tasks demonstrate that TCSM matches or surpasses current methods. Additionally, TCSM is versatile, applicable to both pre-training and post-training scenarios, offering greater flexibility and sample efficiency.

Diffusion language models (DLMs) provide a bidirectional generation framework naturally suited for infilling, yet their performance is constrained by the pre-specified infilling length. In this paper, we reveal that DLMs possess an inherent ability to discover the correct infilling length. We identify two key statistical phenomena in the first-step denoising confidence: a local Oracle Peak that emerges near the ground-truth length and a systematic Length Bias that often obscures this signal. By leveraging this signal and calibrating the bias, our training-free method CAL (Calibrated Adaptive Length) enables DLMs to approximate the optimal length through an efficient search before formal decoding. Empirical evaluations demonstrate that CAL improves Pass@1 by up to 47.7\% over fixed-length baselines and 40.5\% over chat-based adaptive methods in code infilling, while boosting BLEU-2 and ROUGE-L by up to 8.5\% and 9.9\% in text infilling. These results demonstrate that CAL paves the way for robust DLM infilling without requiring any specialized training. Code is available at https://github.com/NiuHechang/Calibrated_Adaptive_Length.

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.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD