Masked Diffusion Models

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21 papers in the last four weeks, up 250% on the four weeks before. 0.2% of all new papers.

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Latest papers 112

Oct 5, 2026cs.AI

DiMOS: Doob-Guided Inference-Time Multi-Objective Search for Scientific Design

Scientific design often requires jointly satisfying multiple objectives and constraints. Pretrained masked diffusion models provide a generative foundation for this task, but fine-tuning them to meet these objectives and constraints incurs additional training costs, motivating inference-time guidance with frozen models. However, such guidance faces two challenges: pass-or-fail constraints and black-box reward models may provide no useful gradients, while jointly satisfying multiple requirements can leave a small feasible region, making feasible designs difficult to find within a limited inference budget. To address these challenges, we introduce DiMOS, a training-free framework for multi-objective scientific design. Using joint rewards from candidate completions, DiMOS performs approximate Doob-guided local resampling without requiring reward gradients. To allocate computation efficiently, it uses budget-efficient trajectory search to focus computation on promising continuations. Across six DNA, protein, and RNA tasks, DiMOS attains the highest joint success rate at comparable generation times, up to

1.98\times

the strongest baseline on DNA and protein, while maintaining high sequence uniqueness and naturalness.

Ziqing Wang, Qijie Zhu, Weimin Wu +4

Northwestern University

Masked Diffusion Models Inference-Time Search Molecular Generation Multi-Objective Optimization Inference-Time Guidance

Oct 4, 2026cs.CV

CleanMDM: Clean Motion Diffusion Model for Multimodal Motion Cleanup

Motion capture data is rarely directly usable, as they typically exhibit missing segments, jitter, drift and contact artifacts. Traditionally, corrupted motions are cleaned by animators through the manual identification of keyframes from noisy motion, subsequent keyframe correction, and interpolation between corrected keyframes to reconstruct coherent motion. While the rise of generative motion models has made automatic cleanup feasible, most approaches operate as black box denoisers with limited controllability, making it difficult to preserve reliable segments or enforce specific user intents. Inspired by animation workflows, we present CleanMDM, a unified multimodal motion cleanup framework that formulates cleanup as masked conditional generation with plug-and-play conditions. This single model supports arbitrary combinations of noisy 3D motion, sparse 2D keyframes, sparse 3D keyframes, and text. This design enables both automatic cleanup without additional user annotation and controllable cleanup under multimodal guidance. To further improve motion realism, we incorporate the Latent Motion Quality Discriminator (LMQD) to better match kinematic distributions and reduce skating, jitter, and interpenetration artifacts, and we apply Mesh-Aware Contact Projection as a test-time optimization step to enhance contact and physical consistency. Experiments across multiple datasets demonstrate that CleanMDM consistently outperforms prior cleanup and generation baselines, and that low cost conditions (text and 2D keyframes) provide reliable controllability gains in multimodal cleanup scenarios.

Zhe Li, Shicheng Wang, Bowen Cai +1

Peking University · Light Origins · Alibaba

Masked Diffusion Models Motion Diffusion Models Multimodal Diffusion Models

Sep 30, 2026cs.LG

Fork-dLLM: Avoiding the Flexibility Trap in Diffusion Language Models

Masked diffusion language models (dLLMs) have shown strong potential for faster inference through parallel token generation when combined with confidence-based samplers. However, recent work has shown that such methods can defer unmasking high-entropy fork positions at which multiple plausible continuations exist. This results in reduced generation diversity, as shown by worse pass@k scaling, and limits gains obtainable from RL post-training. To avoid this flexibility trap, prior work advocated for autoregressive (AR) sampling. Here, we show that discarding confidence-based sampling is unnecessary and, once inference cost is taken into account, wasteful. We first propose Fork-dLLM, a simple hybrid sampler that uses AR-style ordering only at uncertain fallback steps while retaining parallel generation otherwise. We then extend the same principle to post-training with ForkGRPO, which uses Fork-dLLM rollouts and applies the GRPO objective only at fallback steps, preserving exact policy-likelihood ratios while substantially reducing rollout and optimization cost. In our experiments, Fork-dLLM matches the strong pass@k scaling of AR sampling while being 2-3x more efficient, and ForkGRPO achieves downstream performance comparable to or better than AR-based GRPO baselines at a substantially lower training cost.

Stipe Frković, Metod Jazbec, Christian A. Naesseth

University of Amsterdam · UvA-Bosch Delta Lab, University of Amsterdam

Masked Diffusion Models Speculative Decoding for Diffusion Language Models Diffusion Language Model Decoding RL for Diffusion Models Diffusion Model Inference Acceleration

Sep 30, 2026cs.LG

CDMD: A Cross-Dataset Mixed-Type Diffusion Model for Tabular Data

Generative models for tabular data are typically trained separately for each dataset, limiting knowledge transfer and requiring the storage of many specialized models. In this paper, we introduce CDMD, a tabular diffusion model trained jointly across heterogeneous datasets with different schemas and variable numbers of numerical and categorical features. Unlike existing cross-dataset tabular diffusion models that operate in continuous representation spaces, CDMD defines diffusion directly over the mixed-type feature space and is trained end-to-end. To accommodate heterogeneous categorical domains, we introduce a schema-restricted reverse-process parameterization for masked diffusion models, in which the output space dynamically adapts to each feature's vocabulary. We then compose numerical and categorical feature-level diffusion processes into a schema-dependent row-level process. A shared schema-aware Transformer denoiser captures dependencies between features and parameterizes the reverse process across varying schemas. On seven real-world datasets, a single jointly trained CDMD achieves the highest average generation quality among strong single-dataset and cross-dataset baselines, while using substantially fewer total parameters than the collection of separately trained models. Furthermore, pre-training on a corpus of 337 datasets improves generation on previously unseen datasets under both limited target data and limited adaptation epochs. These results demonstrate the potential of direct mixed-type diffusion for shared and transferable tabular data generation. Our code is available at https://github.com/ketatam/cdmd.

Mohamed Amine Ketata, Maximilian Schambach, Stephan Günnemann

Munich Data Science Institute, Technical University of Munich, Germany · SAP SE, Germany

Masked Diffusion Models Tabular Diffusion Models Synthetic Tabular Data Generation Diffusion Models

Sep 29, 2026cs.AI

Conditional Generation of Creative Chess Puzzles with Diffusion Models

While modern language models demonstrate impressive generative capabilities, they often struggle with constrained, counter-intuitive creative tasks. To address this limitation, we explore chess puzzle generation as a rigorous testbed for computational creativity and reasoning, a domain where altering a single piece can invalidate an entire solution. We propose a novel approach for conditional generation of creative chess puzzles using masked diffusion models. Unlike previous methods, our non-directional diffusion approach allows for conditioning on specific tactical themes and partial board positions. We introduce a novel auxiliary task of simultaneous best-move prediction, which improves solution uniqueness by 11.6% and theme-conditioning accuracy by 2.5%. To further optimize solution uniqueness and theme conditioning, we establish a reinforcement learning framework adapted from Denoising Diffusion Policy Optimization (DDPO). This RL training increases the yield of unique and theme-matching positions by 89.1%. Finally, we release the first open-weights models (Appendix B) for chess puzzle generation, offering a new pathway for controllable, creative generation.

Aatu Selkee, Severi Rissanen, Xidong Feng +2

Aalto University · Google DeepMind

Masked Diffusion Models Computational Creativity Chess Conditional Generative Modeling

Sep 29, 2026cs.AI

Fine-Tuning Diffusion Language Models with Context Selection and Target Weighting

Supervised fine-tuning of discrete diffusion language models masks some response tokens and trains the model to recover their original values from the visible context. The masking pattern therefore determines both the context available to the model and the tokens it learns to predict. Uniform random masking does not explicitly account for the interaction between these choices. We introduce GoldiMask, which selects tokens to reveal as context by approximately maximizing a submodular objective. This objective uses model signals to balance the benefit of revealing tokens against their value as prediction targets. GoldiMask then weights the remaining targets according to how they benefit from the selected context and their remaining learning potential. Across three backbones and three training datasets, GoldiMask achieves the highest average accuracy in most evaluated settings, demonstrating gains on both reasoning and code generation. Component ablations show that both context selection and target weighting contribute to the gains. GoldiMask also reduces decoding iterations on GSM8K and MATH-500 under confidence-threshold parallel decoding, while maintaining comparable accuracy at higher confidence thresholds.

Loay Mualem, Lluís Pastor-Pérez, Vinh Tong +4

IMPRS-IS · Institute for AI, University of Stuttgart · Bitdefender

Masked Diffusion Models Diffusion Model Fine-Tuning Diffusion Language Models

Sep 29, 2026cs.LG

On Trajectory-Aware Training for Masked Diffusion Language Models

Masked diffusion models (MDMs) generate text by unmasking several tokens per step, but they are trained and sampled under different conditions. The model is trained on randomly masked sequences, whereas inference follows a trajectory shaped by the model's own predictions. Additionally, each step has no access to what the previous one computed. Recent methods narrow these limitations from separate angles, leaving open how these choices interact. We introduce PUMBA, a unified framework for trajectory-aware training that trains the denoiser on consecutive steps of policy-induced trajectories, passes information between steps, and optimizes them jointly by backpropagation through time. A controlled study of this design space shows that i) exact train--inference alignment fails due to local overfitting, whereas a looser alignment still brings training masks closer to those seen at inference; ii) passing continuous information outperforms discrete gradient estimators through the commitment at each step; and iii) performance improves as backpropagation through time spans more steps, which we support theoretically. Combined, these components match the best checkpoint of a same-size autoregressive model. Building on these findings, we scale PUMBA to supervised fine-tuning of LLaDA-8B, where it improves the trade-off between performance and number of function evaluations (NFEs) in both full-canvas and block diffusion generation. At matched performance, it needs up to 22% fewer NFEs than standard fine-tuning with twice the budget in full-canvas generation, and up to 26% fewer than standard fine-tuning for the same number of steps in block diffusion.

Manuel Madeira, Amitis Shidani, Alice Bizeul +6

EPFL · Apple · Georgia Institute of Technology

Masked Diffusion Models Diffusion Language Model Inference Diffusion Model Fine-Tuning Diffusion Language Models

Sep 29, 2026cs.CL

E-MoE: Enhanced Mixture-of-Experts for Non-Factorized Diffusion Language Models

Masked diffusion models (MDMs) generate sequences by progressively unmasking several tokens per denoising step, but their reverse process is typically factorized over positions, limiting sample quality in the few-step regime where diffusion's speed advantage over autoregressive decoding matters most. A recent line of work introduces a continuous Gaussian latent, trained as a variational autoencoder, to capture correlations across positions, but such approaches are prone to posterior collapse, where the latent is silently ignored. We propose Enhanced Mixture-of-Experts (E-MoE), which builds the reverse process as a mixture of factorized distributions over a discrete shared latent given by the expert-routing decisions of a Mixture-of-Experts (MoE) backbone, without increasing active parameters over the factorized baseline. Across synthetic multi-modal benchmarks, binarized MNIST, and LM1B, E-MoE improves few-step generation over factorized baselines.

Arseny Ivanov, Alexander Kolesov, Alexander Korotin +2

AXXX, Moscow, Russia · Applied AI Institute, Moscow, Russia

Masked Diffusion Models Few-Step Diffusion Sampling Diffusion Language Models Mixture-of-Experts Models

Sep 29, 2026cs.SE

How Should Diffusion Language Models Edit Code?

Code editing requires a model to decide where to make changes, generate the new content, and preserve everything else. We study how masked diffusion language models divide these responsibilities across four editing interfaces: whole-file rewriting, search-and-replace, locate-then-infill, and token-level editing. Experiments on CanItEdit reveal a composition gap: diffusion models can generate coordinated changes when the correct edit locations are supplied, but much of this capability is lost when those locations must be predicted. Access to the intact original code helps the model fill multiple edit regions, yet does not resolve the difficulty of selecting those regions. By varying the editable regions while holding the generation model and decoding procedure fixed, we identify two distinct requirements for successful editing: covering every required change and placing precise boundaries around it. Missing a required region prevents the corresponding change, while widening regions to ensure coverage can sharply reduce success by requiring unchanged code to be regenerated. A sentence-level Wiki editing probe shows the same qualitative gap between supplied and predicted locations beyond code. These findings show why strong infilling capability alone does not ensure reliable editing: the interface must expose all required changes while limiting regeneration of unchanged code.

Xijia Tao, Ziru Liu, Shansan Gong +7

The University of Hong Kong · Huawei Technologies Ltd. · City University of Hong Kong +1

Masked Diffusion Models Language Model Editing

Sep 29, 2026cs.CL

Reliable Parallel Decoding in Masked Diffusion Language Models

Masked diffusion language models (MDLMs) can generate text efficiently by predicting multiple masked tokens in parallel, but predictions from the same forward pass are not necessarily reliable when committed together. We study when parallel commitment is reliable. Our diagnostics show that confidence alone does not determine a reliable commitment order: confident predictions near the end of the sequence can fix an answer before its supporting computations are established, and downstream predictions become less reliable as the uncertainty of their upstream context grows. At the same time, a single forward pass can already resolve several masked tokens, and predictions that remain stable across the final layers are more likely to be correct. Based on these findings, we propose Reliable Parallel Decoding (RPD), a training-free method that selects candidates by layerwise prediction stability and final confidence, and commits them under a cumulative entropy budget over their preceding masked positions. RPD defers predictions with uncertain upstream context while committing the remaining candidates in parallel, without relying on a fixed block schedule. Across mathematical reasoning and code generation benchmarks on LLaDA and Dream, RPD achieves the highest decoding throughput among the evaluated methods while maintaining or improving accuracy.

Zhenghao He, Bohan Liu, Guangzhi Xiong +1

Department of Computer Science, University of Virginia

Masked Diffusion Models Diffusion Language Model Decoding

Sep 28, 2026cs.LG

Twist, Don't Tilt: Trajectory-Exact Constrained Decoding for Masked Diffusion Models

Constrained decoding for Masked Diffusion Language Models (MDLMs) aims to ensure that generated outputs satisfy a specified structure or syntax constraint. MDLMs generate outputs by repeatedly unmasking masked positions present in their current state. Recent strategies for constrained decoding constrain the model's per-step mean-field posterior (which factorizes over masked positions) by enforcing the desired constraint with an automaton. The resulting chain-structured factor graph allows exact constrained sampling via dynamic programming. However, despite each draw being exact and constraint-satisfying, we prove that their composition, in general, tilts away from the model's relative probabilities over valid trajectories, thus leading to trajectory bias. We derive an exact expression for this bias as a product of ratios measuring how valid continuation mass changes when the denoiser is reconditioned, and characterize when the bias vanishes. We then correct the bias by introducing TWISTER, the first automaton-twisted Sequential Monte Carlo decoder for MDLMs, using the step-exact decoder as the proposal. We show that for regular language constraints, the Feynman-Kac correction is exactly computable, with the twists obtained efficiently using quantities pre-computed for step-exact sampling. We prove that the resulting Feynman-Kac model targets the unbiased Doob h-transformed path law conditioned on constraint satisfaction.

Aditya Thimmaiah, Lara Marinov, Jayanth Srinivasa +3

The University of Texas at Austin · Cisco Research

Constrained Decoding Masked Diffusion Models Language Model Decoding Diffusion Language Model Decoding

Sep 28, 2026cs.CV

DiMoP: Diffusion-Driven Motion Representation Learning With Frame-Level Pseudo-Classification for Skeleton-Based Action Recognition

Robust skeleton-based action recognition requires representations that capture a wide spectrum of motions, from subtle to moderate and strong ones. Existing methods often focus on strong motions. This paper introduces DiMoP, a masking- and diffusion-driven motion representation learning method with frame-level pseudo-classification to explicitly learn the distribution of joint motions rather than regressing deterministic coordinates, as existing methods often do. By diffusing masked joints with progressive noise and denoising them conditioned on visible joints, DiMoP learns through controllable noising and denoising processes, enabling uniform learning of weak, moderate, and strong dynamics. To enable the masking-based generative diffusion learning with a discriminative capability, a pseudo-frame classifier is proposed that enforces the learning towards sequence-consistent and temporally coherent pseudo-labels without manual annotations. Together, these strategies provide a principled mechanism for joint generative and discriminative motion modeling. DiMoP achieves state-of-the-art performance across NTU RGB+D 60/120, and PKUMMD, including a 1.1 percentage point gain over prior works on NTU RGB+D 120 with the cross-subject protocol.

Shanaka Ramesh Gunasekara, Wanqing Li, Nikalal Kaldera +2

Advanced Multimedia Research Lab, University of Wollongong, Australia

Skeleton-Based Action Recognition Masked Diffusion Models Motion Representation Learning

Sep 28, 2026cs.CV

BiMoGen: Bidirectional Motion-Text Generation via Unified Masked Discrete Diffusion

Text-to-motion generation and motion-to-text captioning are two fundamental tasks in human motion modeling, both grounded in the same underlying motion-text correspondence. Existing unified approaches mostly rely on autoregressive modeling, which imposes a fixed generation order and is therefore poorly suited to the bidirectional dependencies between language and motion, allowing early prediction errors to persist as fixed context and degrade both temporal coherence and cross-modal consistency. Masked discrete diffusion, which models sequences through iterative bidirectional prediction, offers a natural remedy. We therefore propose BiMoGen (Bidirectional Motion-text Generation), a unified masked discrete diffusion framework for bidirectional motion-text modeling. To stabilize training, we design Decoupled Uni- and Cross-Modal Training, in which masked pretraining first establishes cross-modal correspondence on paired motion-text sequences, after which supervised fine-tuning specializes the model for bidirectional generation. Masked diffusion nonetheless introduces its own source of error, as the model is trained on clean ground-truth context yet encounters self-generated and potentially erroneous context at inference, with errors committed under heavily masked states propagating through subsequent steps. We further introduce Generation-Aware Self-Correction that exposes the model to its own predictions during training and applies correction passes at early sampling steps to revise unreliably committed tokens. Extensive experiments on HumanML3D and KIT-ML demonstrate competitive performance on both tasks, validating the effectiveness of the proposed two-stage training and self-correction designs. The project page is available at https://wengwanjiang.github.io/BiMoGen-Page.

Wanjiang Weng, Yongliang Wu, Xiaofeng Tan +3

Department of Computer Science and Engineering, Southeast University, Nanjing, China · Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, Nanjing, China · National University of Singapore +1

Masked Diffusion Models Text-to-Motion Generation Human Motion Generation Diffusion Models for Motion Generation Multimodal Diffusion Models

Sep 28, 2026cs.LG

TANGO: Watermarking Masked Diffusion Language Models in Token Pairs

Masked-diffusion language models fill in masked positions in parallel and in no fixed order. Most practical text watermarks assume left-to-right generation. They key each token to the tokens before it, and in a diffusion model those tokens may still be masked. A fixed green list needs no such context, but it favors the same tokens at every position, so these tokens appear more often in watermarked text. An attacker who compares token frequencies in watermarked and unwatermarked text can recover the list and forge text that the provider's own detector accepts. We present TANGO, a watermark for masked-diffusion language models that keys each new token to a nearby token that is already unmasked. A secret key splits the vocabulary into color classes, and TANGO biases the new token toward a color determined by the key and the nearby token's color. The watermark is therefore embedded in pairs of tokens. Because the favored color changes from position to position, token frequencies stay much closer to those of unwatermarked text than under a fixed green list. Detection needs only the text and the key, and it does not assume any unmasking order. On two masked-diffusion models, TANGO detects nearly all unedited watermarked texts and most edited ones, and frequency attacks that forge the fixed green list fail against it.

Kasra Arabi, Nir Weinberger, Micah Goldblum +1

Diffusion Model Watermarking Masked Diffusion Models LLM Watermarking Robustness of Machine-Generated Text Detection

Sep 28, 2026cs.LG

Low-Confidence Remasking Traps Flexibility: Realizing Arbitrary-Order Potential for Diverse Rollouts in Diffusion LLMs

Masked diffusion language models support arbitrary-order generation, suggesting a natural way to produce diverse outputs. However, recent work argues that this flexibility reduces diversity by delaying high-uncertainty tokens that can lead to different generation paths. We trace this diversity loss not to arbitrary-order generation itself, but largely to low-confidence remasking (LCR), a widely used decoding rule. At each step, LCR samples a token at every masked position but commits only the sampled token with the highest probability, filtering out the rest. We show that this mechanism can exponentially suppress lower-probability tokens as more positions compete, and observe the same suppression in LLaDA. In contrast, top-probability position selection (TPP), which has often been conflated with LCR under the shared label confidence-based decoding, avoids this diversity loss. TPP first selects the position whose most likely token has the highest probability, then samples directly from that position's distribution. Replacing LCR with TPP restores diversity and yields Pass@

k

comparable to left-to-right decoding, suggesting that the reported diversity loss stems largely from LCR's filtering rather than from generating high-confidence positions first. To further exploit order flexibility, we introduce Entropy-Guided Initialization (EGI), which samples the first token at the highest-entropy position and then follows TPP. This simple modification further improves rollout diversity and solution coverage beyond left-to-right decoding, with gains extending to downstream policy optimization, highlighting the potential of arbitrary-order generation for diverse rollouts.

Moongyu Jeon, Dongjae Jeon, Bumjun Kim +2

Yonsei University · KRAFTON AI · Kookmin University

Masked Diffusion Models Diffusion Language Model Decoding Diffusion Language Models

Sep 28, 2026cs.LG

One Sequence, Many Decodings: CAGenMol-2 Recasts Drug Design as Masked Molecular Inference

Drug design couples property evaluation, conditional generation, structure-based design, and local optimization, yet machine learning systems typically address these capabilities with separate task-specific models. We introduce CAGenMol-2, a masked diffusion molecular language model that represents molecules, continuous scalar properties, and 3D protein pockets within a single wrapped sequence. Within this pretrained interface, downstream operations are selected by which sequence regions are observed or masked at inference, allowing one checkpoint to perform property prediction, property- and pocket-conditioned generation, and partial-constraint design without task-specific architectures or backbone fine-tuning. We further propose Adaptive Fragment Optimization (AdaFO), a gradient-free mask-and-refill search that turns the masked decoder into an iterative local molecular optimizer. On CrossDocked2020, AdaFO increases Success Rate from 30.2% to 70.8%, the best reported under this protocol, while largely preserving drug-likeness and diversity. Finally, scaffold-preserving directional editing and CRBN/VHL case studies demonstrate its use in compound design workflows spanning local molecular editing, structure-based prioritization, and downstream simulation-based screening.

Yanting Li, Enyan Dai, Lei Wang +2

The Hong Kong University of Science and Technology (Guangzhou) · Jinan University, Guangzhou

Molecular Optimization Masked Diffusion Models Structure-Based Drug Design Molecular Generation Molecular Property Prediction

Sep 27, 2026cs.CL

Simple Diffusion Language Models Are More Effective Few-Step Generators Than Reported

Diffusion language models (DLMs) promise fast parallel generation, yet high-quality samples often require large number of refinement steps, which diminishes their advantage in practice. This has led to massive interest in and rapid development of new methods for effective few-step generation. We show that much of the supposed quality gap at few steps can instead arise from a suboptimally configured sampler. Modest sampler sharpening, without any model retraining, enables a couple years old masked DLM to rival supposedly far improved successors. This differently sampled DLM in fact achieves lower generative perplexity in just 16 steps than what its standard sampler obtains with 1024, while improving both judged quality and semantic diversity. We further show that conventional per-output metrics can fundamentally obscure these gains, since any optimal trade-off between two such metrics can be attained by a generator supported on at most two outputs. We subsequently introduce GroupEval, which separately evaluates quality and across-output semantic diversity, and offers fresh insights including uncovering how 1.5-4.7x perplexity gains of a distilled model yield no corresponding quality gain. Finally, we explain why sharpening helps: parallel unmasking destroys dependencies among simultaneously generated tokens, creating a gap between prediction and generation. We prove that pervasive temperature choice of one is generically suboptimal under parallel sampling even for an exact denoiser, and that worse predictions can yield better samples. Through these results, we argue for a broader evaluation principle of treating the deployed generator as the object of comparison, benchmarking it against tuned baselines, and assessing quality and diversity jointly and with more human-aligned measures.

Hasan Amin, Ming Yin, Rajiv Khanna

Purdue University

Masked Diffusion Models Language Model Generation Evaluation Diffusion Sampling Few-Step Diffusion Sampling Parallel Decoding Diffusion Language Models

Sep 27, 2026cs.AI

Unmask the State: When Does State Adaptation Matter for Masked Diffusion Language Models

Masked diffusion language models (MDMs) admit flexible generation orders, making the unmasking strategy an inference decision. Existing methods vary in how they prioritize positions, control parallelism, restrict selection regions, revise predictions, or plan future denoising, yet it remains unclear when these choices should change during generation. We study this question through strategy reversals, where an alternative action becomes preferable to a fixed choice. We organize MDM inference into five axes--score, cardinality, region, commitment, and planning--and define adaptation opportunity as the one-step utility advantage of the best candidate action over a validation-selected fixed action. This view shows that adaptation value depends on both the frequency and magnitude of such reversals. Across three MDMs and ten tasks, adaptation opportunities are highly heterogeneous, with some regimes exhibiting concentrated and predictable one-step gains. This motivates selective adaptation: lightweight detectors calibrated on validation prompts identify high-opportunity states, capturing, for example, 56.9 percent of the candidate-set oracle opportunity by adapting only the top 10 percent of states on LLaDA-8B constrained JSON filling. Our transition-level results suggest that state adaptation is most useful when applied selectively rather than uniformly.

Injin Kong, Sunghwan Choi, Yohan Jo

Graduate School of Data Science, Seoul National University

Masked Diffusion Models Diffusion Language Model Inference Diffusion Language Model Decoding

Sep 18, 2026math.ST

Schedule optimization for tau-leaping in masked discrete diffusion

Masked diffusions are popular generative models for discrete distributions. Unlike standard autoregressive sampling, they reveal several coordinates in parallel, approximating each block's joint conditional law by a product of one-coordinate conditionals. The resulting procedure, usually called tau-leaping, reduces computational cost but introduces a factorization error (

\varepsilon_\text{fact}

), even with perfectly learned predictors. We study the resulting tradeoff between generative accuracy and computational cost, focusing on how to choose a denoising schedule to minimize

\varepsilon_\text{fact}

for a fixed sampling budget. To do so, we establish an exact integral representation of

\varepsilon_\text{fact}

separating the schedule from the target's dependence structure, summarized by a dependence density

ρ

. This representation yields recursive stationarity equations for optimal schedules and allows us to quantify how estimation errors in

ρ

affect schedule selection. As the dimension

N

and sampling budget grow, we characterize the optimal schedule and quantify the cost of random block sizes relative to a deterministic planner. We highlight a fundamental dichotomy: if

ρ

converges uniformly to a strictly positive continuous profile as

N\to\infty

, schedule optimization can only improve the leading constant of

\varepsilon_\text{fact}

, while if

ρ

degenerates, schedule optimization can improve the asymptotic order. Examples based on stationary processes and exchangeable mixtures illustrate these regimes.

Cecilia Secchi, Giacomo Zanella

Bocconi University, Department of Decision Sciences, Milan, Italy. · Bocconi University, Department of Decision Sciences and BIDSA, Milan, Italy.

Masked Diffusion Models Diffusion Sampling Diffusion Timestep Scheduling

Sep 17, 2026cs.LG

Parallelism, critical windows, and separations among diffusion language models

A popular selling point of diffusion large language models (dLLMs) is their capacity for parallelism: the ability to generate sequences of text far more efficiently than autoregressive models, which require one forward pass per token. Yet among the many competing paradigms for dLLMs, from masked to uniform to Gaussian diffusion, principled understanding of how these different proposals compare in parallelism remains limited. In this work, we initiate a fine-grained comparison of the capacity for parallelism among these three leading approaches and prove the following: - Uniform and Gaussian diffusion can sample in a number of forward passes which scales with the dual total correlation of the underlying distribution, a measure of intrinsic complexity which can be much smaller than the context length. Previously, it was only known how to achieve this using masked diffusion. - For a certain family of random empirical measures, we show that

\widetildeΘ(\sqrt{d})

forward passes are necessary and sufficient to sample using uniform or Gaussian diffusion, yet there exist approximate score oracles for which

\widetildeΩ(d)

forward passes are needed for masked diffusion. This establishes the first provable separation in parallelism between the three prevailing dLLM paradigms. Contrary to popular intuition that masked diffusions are harder to parallelize because they must commit to token values, the latter separation instead comes from the fact that the critical windows in masked diffusion sampling are asymptotically narrower than those in uniform and Gaussian diffusion sampling.

Sitan Chen, Liye Wang

SEAS, Harvard University · Tsinghua University

Masked Diffusion Models Diffusion Sampling Diffusion Language Model Inference Diffusion Language Model Decoding Diffusion Language Models Continuous Diffusion Language Models

Sep 17, 2026cs.CL

Zarya: A Hybrid Autoregressive--Masked Diffusion Language Model with Flexible Training and Dual-Mode Inference

Autoregressive language models (ARMs) are constrained by sequential, left-to-right generation, while masked diffusion models (MDMs) enable parallel decoding but suffer from high computational overhead due to the inability to reuse Key-Value (KV) cache and from incoherent generation arising from learning dependencies over an intractable space of token combinations. We introduce Zarya, a family of hybrid language models that jointly optimizes an autoregressive (AR) objective and a masked-diffusion objective within a single architecture. Zarya structures training data into variable-size slots and employs a curriculum that gradually increases slot granularity, enabling a smooth transition from fine-grained AR learning to coarse-grained diffusion learning. At inference, Zarya provides two distinct decoding paradigms through a unified interface: (i) MDM sampling with first-hitting denoising, and (ii) slotted speculative decoding that interleaves inter-slot diffusion-based selection with intra-slot autoregressive infilling, achieving full KV cache reuse. The training and inference regimes are fully decoupled, allowing a model trained with any configuration to be deployed in either mode. Extensive configurability --- including grouped noise patterns (Prefix Completion, Fill-In-the-Prefix, Fill-In-the-Middle), ordered sampling schedules, and noise-level permutation strategies --- enables flexible research exploration. We release Zarya models publicly in sizes 0.6B, 1.7B, and 4B, demonstrating performance on standard benchmarks while offering a principled integration of autoregressive and diffusion paradigms.

Leonid Sinev, Ilya Koziev, Vladislav Leshchuk

Masked Diffusion Models Autoregressive Diffusion Diffusion Language Model Decoding Diffusion Language Models Diffusion Model Inference Acceleration

Sep 14, 2026cs.CL

Representation-based Masked Diffusion Model

Masked Diffusion Models (MDMs) have emerged as a compelling paradigm for language modeling, offering the capability for efficient parallel text generation. However, existing parallel sampling methods typically update multiple masked tokens independently and ignore the complex mutual dependencies among the masked tokens. This independent updating mechanism lacks global coordination and might lead to incoherent outputs. To address this limitation, we propose Representation-based Masked Diffusion Model (RMDM), a framework that leverages the text representation to explicitly encode global semantics and help to parallel update tokens more precisely. Specifically, we first encode text into a continuous semantic space using a pretrained encoder and learn an invertible transformation that normalizes the representation distribution to a Gaussian prior, facilitating efficient sampling during generation. Conditioned on this latent semantic representation, we train a masked diffusion model to learn the conditional text distribution, where the representation serves as global semantic guidance to coordinate parallel token updates and faithfully approximate the target distribution. Empirical results demonstrate that RMDM significantly improves generation quality, particularly in aggressive few-step sampling regimes.

Yangrong Hu, Ding Huang, Xueyu Zhou +1

Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University, Hong Kong SAR, China · Department of Applied Mathematics The Hong Kong Polytechnic University, Hong Kong SAR, China · ByteDance Seed, Beijing, China

Non-Autoregressive Text Generation Masked Diffusion Models Few-Step Diffusion Sampling Diffusion Language Models

Sep 3, 2026cs.IR

EPIC: Explicit Posterior Item Conditioning for Semantic ID Diffusion Recommendation

Semantic ID (SID) generative recommendation predicts the next item by generating a short tuple of discrete tokens. Recent masked-diffusion methods improve this process through bidirectional context and flexible decoding, yet recommendation ultimately requires selecting among complete catalog items. At each denoising step, a partial SID can correspond to multiple feasible items, while existing methods primarily reason through position-wise token predictions. We propose Explicit Posterior Item Conditioning (EPIC), which introduces explicit item-level competition into SID denoising. EPIC constructs a personalized posterior over feasible candidate items using the current generation context and the user's recent interactions, then projects this distribution back to unresolved SID positions to guide subsequent token decisions. The pretrained backbone remains frozen and requires no additional decoder forward pass. Experiments on four Amazon benchmarks show consistent improvements over strong baselines, while diagnostic analyses indicate that the gains primarily arise from personalized transition evidence that preserves promising item hypotheses during denoising.

Tuan-Binh Tran, Thanh Tam Nguyen, Quoc Viet Hung Nguyen +3

College of Engineering and Computer Science VinUniversity Hanoi, Vietnam · School of Information and Communication Technology Griffith University Gold Coast, Queensland, Australia · Department of Computer Science Aalborg University Copenhagen, Denmark

Semantic ID Recommendation Sequential Recommendation Diffusion Model Guidance Masked Diffusion Models

Aug 31, 2026cs.AI

CARVE: Verified Expansion for Variable-Length Generation in Diffusion Language Models

Masked diffusion language models predict tokens from a partially observed response canvas, enabling bidirectional conditioning and parallel token refinement. Yet standard masked-diffusion decoders use a rigid inference interface: the number of masked positions allocated to the answer is fixed before generation begins. Choosing this length is difficult. A short canvas can truncate reasoning or code, while a long canvas wastes computation and can perturb denoising. We introduce CARVE (Counterfactual-Aware Reveal with Verified Expansion), a training-free variable-length algorithm for masked diffusion LMs. Starting from a shorter canvas, CARVE can grow the response during decoding by inserting additional [MASK] positions. Rather than keeping every insertion, CARVE tests a candidate expanded canvas and asks a counterfactual question: would the model make similar predictions for the unresolved positions in the original canvas if the extra masked space were present? The inserted masks are kept only when they induce low Jensen-Shannon (JS) divergence on aligned unresolved positions. This makes length growth a verified stability decision rather than a pure confidence heuristic. CARVE applies without retraining to both full-canvas and blockwise diffusion decoders. Across code generation and mathematical reasoning benchmarks, CARVE consistently improves average performance over fixed-length baselines across all evaluated model families. Crucially, CARVE achieves these accuracy gains while reducing inference cost, reaching half the FLOPs of fixed-length decoding in some settings.

Wail Bouhedja, Amr Mohamed, Guokan Shang

1MBZUAI · 2Sorbonne Université · 3Ecole Polytechnique

Masked Diffusion Models LLM Inference Acceleration Diffusion Language Model Decoding Diffusion Language Models LLM Code Generation LLM Reasoning

Aug 31, 2026cs.AI

DiffPDE: Masked Diffusion Language Models as PDE Solver

Existing approaches for synthesizing Partial Differential Equation (PDE) solvers predominantly rely on autoregressive models, yet their global left-to-right decoding incurs substantial redundancy when addressing inherently localized bugs. In this work, we challenge this inefficient paradigm and propose DiffPDE, a framework leveraging discrete diffusion language models for targeted code repair. By introducing a localized re-masking and infilling strategy, DiffPDE regenerates only erroneous regions while preserving correct context, naturally aligning generation with the sparse nature of PDE errors. Furthermore, to handle coupled bugs requiring sequential interventions, we present Iterative Debugging GRPO (ID-GRPO), a reinforcement learning scheme that enables multi-round debugging within single trajectories via intermediate rewards. Experiments on PDEBench show that DiffPDE achieves competitive accuracy, outperforms same-scale AR models, and significantly accelerates repair.

Wenxuan Guo, Yuyang Hong, Lubin Fan +4

School of Artificial Intelligence, University of Chinese Academy of Sciences · MAIS, Institute of Automation, Chinese Academy of Sciences · Independent Researcher

RL for Code Generation Masked Diffusion Models Automated Program Repair PDE Solving

Aug 30, 2026cs.CV

Discrete Diffusion Bridges for Spatiotemporally Aligned Image Translation and Generation

We propose Discrete Diffusion Bridges (DDB), a novel framework designed to resolve the fundamental spatiotemporal misalignment of standard discrete diffusion in image translation and generation. By corrupting data into a pure mask state via a random schedule, the conventional forward process induces a twofold misalignment: spatially, this pure-mask destination entirely discards the rich structural priors of the source image; temporally, the random masking order inherently contradicts the ``easy-first, hard-last'' decoding mechanism used during inference. To address this, DDB constructs a direct and efficient trajectory between domains. Spatially, we introduce a hybrid absorption mechanism that redefines the absorbing state to a stochastic mixture of mask and source tokens, effectively injecting source prior as spatial anchors into the latent space. Temporally, we design an information-guided noise schedule that quantifies semantic variation to prioritize the corruption of high-information regions at earlier timesteps. This ensures the model learns to resolve difficult semantic changes using robust context from invariant regions. Extensive experiments validate the versatility and robustness of our framework across diverse generative paradigms. DDB effectively balances edit alignment with structural fidelity across both text-guided semantic manipulation and pure structural image translation, while inherently complementing text-to-image generation and guaranteeing robust high-quality decoding under extremely low sampling steps. Code and models are available at https://github.com/HKU-HealthAI/DDB.

Xing Xie, Jiawei Liu, Shijun Zhou +4

State Key Laboratory of Robotics and Intelligent Systems, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, China · University of Chinese Academy of Sciences, Beijing, China · School of Computing and Data Science, The University of Hong Kong, Hong Kong

Masked Diffusion Models Image-to-Image Translation Diffusion Timestep Scheduling Diffusion-Based Image Editing Diffusion Models

Aug 27, 2026cs.LG

VGAS: Variance-Reduced Guidance and Adaptive Selection for Training-Free Reward Alignment in Discrete Diffusion

Masked discrete diffusion models perform strongly on text, code, and biological sequences, but their training objective rewards only naturalness, and retraining the generator for every new reward is expensive. Inference-time steering of a frozen model either guides the sampler by the reward gradient or searches over several trajectories, and recent samplers combine the two. Such combinations are assembled as pipelines that leave three choices at their defaults: a guidance estimate resting on one Gumbel draw per sample, a reward tilting placed without reference to the distribution the combination then targets, and a selection temperature held fixed although the spread of per-step rewards drifts. We identify that distribution and settle the three choices against it. We therefore propose Variance-reduced Guidance and Adaptive Selection (VGAS), a simple yet effective inference-time framework that reduces the variance of the guidance estimate for both reward types, applies the reward tilting in the clean-token logits, where the pretrained schedule is preserved, and sets the selection temperature per step. Across regulatory DNA, protein and small-molecule benchmarks, VGAS attains the best training-free reward and matches or surpasses a reward-fine-tuned generator.

Kwanyoung Kim

Department of AI, GIST

Diffusion Model Alignment Diffusion Model Guidance Masked Diffusion Models Inference-Time Guidance

Aug 13, 2026cs.LG

The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexity

We study masking diffusion for discrete sampling and introduce a path-resolved measure of data geometry called the \emph{unmasking growth complexity} ({\textsf{UGC}\xspace}). Its local increments directly control Kullback--Leibler (KL) discretization error, yielding a unified analysis of Bernoulli-subset and fixed-cardinality unmasking schemes. In log-reveal-odds coordinates, this structure yields optimized single-block and multi-block schedules, and quantifies the gains from adapting computational effort to data geometry. Crucially, we show how {\textsf{UGC}\xspace} increments can be estimated from samples via KL increments along coupled reveal trajectories. This leads to \emph{certified-optimal} samplers that achieve a prescribed KL error with high probability and iteration complexity within a constant factor of the corresponding oracle procedure. Collapsing the \ugc path yields the aggregate {\textsf{UGC}\xspace} mass, which connects to classical multivariate dependence measures and complexity measures from previous analyses of discrete diffusion. In the fine-partition limit, the squared integral of the square-root {\textsf{UGC}\xspace} density determines the sharp leading-order optimal Euler discretization error. Examples exhibit substantial dimension-dependent gains over coarse schedules, including

\widetildeΩ(\sqrt{d})

improvements achievable with a constant number of adaptively placed blocks.

Martin J. Wainwright

Lab for Information and Decision Systems · Statistics and Data Science Center · EECS and Mathematics

Masked Diffusion Models Diffusion Sampling Diffusion Timestep Scheduling Diffusion Model Acceleration

Aug 7, 2026cs.CL

Stoicheia: Character-Level Masked Diffusion for Ancient Greek Textual Restoration, Parsing, and Metrical Scansion

We introduce Stoicheia, a 405M-parameter character-level masked-diffusion encoder for Ancient Greek whose input factors into five aligned, independently maskable planes: letters, word and sentence boundaries, diacritics, capitalization, and punctuation. A single backbone can therefore restore lacunae, re-segment, accentuate, and punctuate unspaced text without task-specific retokenization. We pretrain it on an open, revision-pinned corpus of 380M words and release eleven checkpoints: ten rotated, decontaminated folds, guaranteeing that for any given literary passage at least one released model has never seen its text, and one with no exposure to documentary texts. Three experiments - reconstruction of damaged inscriptions and papyri, morphosyntactic tagging and dependency parsing, and macronization with metrical scansion - each carry a matched random-initialization control, isolating what character-level diffusion pretraining contributes: 5.6 CER points on inscription reconstruction, 12.9 LAS on parsing, and 6.0 points of balanced accuracy on macronization. On Ithaca's own test split, with identical frozen samples and strict scoring, Stoicheia reduces character error relative to both prior state-of-the-art systems, from 24.6 (Ithaca) and 23.5 (its 2025 Aeneas-framework successor) to 15.5, and raises top-1 accuracy from 63.0 and 64.0 to 74.5.

Eric Cullhed, Albin Thörn Cleland

Department of Linguistics and Philology · Uppsala University · Sweden +2

Masked Diffusion Models Dependency Parsing

Aug 6, 2026cs.CL

Lost in Interpolation: Why Predictive Feedback Fails in Diffusion Language Models

Soft-masking accelerates the convergence of Masked Diffusion Language Models (MDLMs). Existing formulations build this blend with linear interpolation (LERP) in the raw embedding space, which implicitly treats that space as Euclidean. We analyze the embedding space of MDLMs and find that the mask and predicted-token embeddings maintain a near-constant angle of (\approx 73^\circ) throughout training, while embedding norms remain essentially flat across vocabulary-frequency rank. These indicate a hyperspherical geometry, for which LERP is the wrong interpolation primitive. We introduce Spherical Soft-Masking (S-SM), a drop-in replacement that aggregates the top-(k) predictions with a Fr'echet mean on the hypersphere and blends this mean with the mask direction using spherical linear interpolation (SLERP), then restores the native mask norm. We evaluate S-SM on continued pre-training of a released 169M-parameter MDLM checkpoint across a wide range of inference-time step budgets, SLERP feedback avoids the training degradation that LERP feedback induces and delivers MAUVE gains of up to 2x over the vanilla MDLM baseline and 27.5-56.1% over TopK/LERP at various sampling budgets, alongside consistently lower generative perplexity (16.9-19.6% over the baseline), while leaving output entropy and convergence essentially unchanged.

Lavanya Nigam, Ishaan Bansal, Aryan Sood +2

Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

Masked Diffusion Models Diffusion Language Model Decoding Diffusion Language Models Representation Geometry in Language Models

Aug 5, 2026cs.SD

Masked diffusion enables coherent beat tracking

Current neural networks for beat tracking generate invalid outputs, such as consecutive downbeats and erratic tempo changes, even when these are not present in the training data. Heavy post-processing techniques can alleviate these problems, but the original cause of this inconsistent behaviour remains unknown. We hypothesise that it stems from inadequate modelling of multiple plausible output beat grids, resulting in an invalid mixture of competing interpretations. We propose a masked diffusion approach that properly models multiple outputs and enables the model to build coherent predictions through iterative inference. We devise three modifications to standard masked diffusion that enable its application to beat tracking: independent masking of beats and downbeats during training and inference, a balanced masking scheduler for inference, and peak-picking across inference steps. Our approach reduces erratic behaviours and improves beat-tracking performance.

Francesco Foscarin, Filip Korzeniowski, Richard Vogl

Moises AI

Masked Diffusion Models Music Information Retrieval

Aug 4, 2026cs.CL

MDLMPE: Distribution Aware Positional Encoding for Masked Diffusion Language Models

Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.

Tong Ling, Hang Lei, Feng Xiao +5

University Chinese Academic of Science · HUJING Digital Media & Entertainment Group · State Key Laboratory for Novel Software Technology, Nanjing University, China +1

Rotary Positional Embeddings Masked Diffusion Models Positional Encoding Diffusion Language Models

Aug 3, 2026cs.AI

EchoChange: A Diffusion Language Model with Dual Pass Remasking for Factual Remote Sensing Disaster Change Captioning

Bi-temporal remote-sensing disaster change captioning often needs to identify sparse and spatially localized changes across large pre- and post-event scenes and then translate them into coherent, factual descriptions. However, existing change captioning methods always follow an autoregressive decoding paradigm to generate the change description and thus an early misinterpretation of the changed object, event, or spatial relation becomes an irreversible premise for subsequent text, amplifying visual ambiguity into cascading factual errors. To address this limitation, we propose EchoChange, a multimodal discrete diffusion language model that formulates change captioning as iterative masked-token denoising rather than left-to-right generation. By repeatedly revising the entire caption while conditioning on the image pair, EchoChange can reconsider uncertain content and correct imperfect intermediate predictions. We further introduce draft-aware dual-pass training, a progressive masking curriculum, and confidence-guided remasking to align training with iterative inference. Extensive experiments on the RSCC benchmark show that EchoChange substantially outperforms both general-purpose and remote-sensing-specific baselines across lexical and semantic metrics. The EchoChange Project is at https://github.com/sundongwei/EchoChange_Project

Dongwei Sun, Bowen Yao, Yujie Zhang +3

School of Computer Science and Technology and the Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, 710049, China · School of Computer Science and Technology, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China · State Key Laboratory of Remote Sensing and Digital Earth, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing, 100094, China

Remote Sensing Image Understanding Masked Diffusion Models Remote Sensing Image Change Captioning Remote Sensing Change Detection Diffusion Language Models Multimodal Diffusion Models

Jul 30, 2026cs.CV

TongueReenact: Geometry-Anchored Tongue Synthesis for Face Reenactment

Modern face reenactment systems achieve impressive pose and expression transfer using geometry-driven representations. However, they largely ignore tongue dynamics, leading to anatomically inconsistent mouth interiors during speech and expressive motions. We introduce the first framework for cross-identity tongue dynamics transfer in face reenactment. We propose a foundation-model-assisted bootstrapping pipeline that produces a dedicated tongue segmentation model for in-the-wild reenactment without curated annotations. We further introduce a spatially constrained latent masked diffusion model for realistic tongue synthesis, with adaptive mask dilation for seamless mouth boundary transitions. Extensive experiments demonstrate improvements of more than two times over all baselines on every tongue-specific metric. We additionally propose a VLM-based evaluation protocol that replicates expert annotation at scale, confirming perceptual superiority across all ablation variants.

MD Wahiduzzaman Khan, Mingshan Jia, Xiaolin Zhang +2

University of Technology Sydney, Australia · Shandong University of Science and Technology, China

Masked Diffusion Models

Jul 29, 2026cs.LG

From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models

Many discrete reasoning tasks, such as code generation, are inherently non-causal: programmers move between high-level structure and local details, a process we call any-order inference. For autoregressive language models, which lack a native any-order interface, non-causal abilities such as infilling and next-edit prediction require hand-designed mechanisms. Can we instead design models that natively support any-order inference? Masked diffusion models have recently emerged as compelling candidates, as their any-order training objective naturally offers an any-order prediction interface. This interface, however, does not automatically yield any-order inference. We demonstrate that this interface-inference gap stems from positional uncertainty: fixed-canvas, token-level models may know what semantic component should appear without knowing where to place it. In light of this, we propose two complementary approaches: (1) Insertion-based masked diffusion, building on FlexMDM (Kim et al, 2025), relaxes fixed-position commitments via insertions, enabling generation across non-contiguous regions. (2) Latent-space masked diffusion shifts prediction to coarser semantic segments, enabling search over latent generation orders. Empirically, we train a 7B FlexMDM for Python coding and a 125M LatentMDM for GSM8K and show that both approaches induce distinct any-order inference behaviors and improve downstream performance. We release our codebase at https://github.com/SeunggeunKimkr/genuine-any-order.

Seunggeun Kim, Jaeyeon Kim, Taekyun Lee +4

University of Texas at Austin · Harvard University

Masked Diffusion Models Diffusion Language Model Inference

Jul 28, 2026cs.AI

PreDiff-LM: Pretrained Discrete Masked Diffusion Language Modeling with Hybrid Attention

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.

Zhengtao Yao, Runhao Li, Xupeng Chen +12

University of Southern California · New York University · Columbia University +4

Masked Diffusion Models Attention Control in Diffusion Models Diffusion Model Fine-Tuning Diffusion Language Models

Jul 22, 2026cs.CL

Multi-Mask Diffusion Language Models for Few-Step Generation

Masked diffusion models (MDMs) are a promising family of language generators, but achieving high-quality few-step generation remains challenging. In MDMs, all forward trajectories collapse to a single fully masked state, leaving no terminal entropy for consistency-style few-step generation. While recent few-step alternatives based on uniform-state diffusion avoid this degeneracy, it becomes harder to distinguish clean tokens from noise than MDMs, which usually harms modeling quality and training efficiency. In this work, we propose a multi-mask diffusion model (MultiMDM) that preserves the masking structure towards few-step generation. In the forward process, each clean token is first pushed towards a designated mask and then gradually mixes over the mask set. As a result, the backward process has a drafting capability by predicting a designated mask before refining to a clean token. We derive a closed-form ELBO training objective for MultiMDM that supports continual training from pretrained MDMs. In addition, we formulate a purely discrete-state consistency distillation scheme, with a shared-Gumbel coupling to reduce pathwise entropy. Experiments on pretraining and distillation show that MultiMDM provides an effective foundation for principled few-step generation.

Sijin Chen, Yinuo Ren, Heyang Zhao +3

ByteDance Seed · Princeton University · Stanford University +2

Masked Diffusion Models Diffusion Model Distillation Few-Step Diffusion Sampling Consistency Distillation Diffusion Language Models Diffusion Models

Jul 20, 2026cs.LG

MotifRole-Diff: Risk-Optimal Role-Aware Corruption for Masked Molecular Graph Diffusion

Masked discrete diffusion for molecular graph generation typically applies a uniform corruption schedule to all tokens in a lossless graph-to-sequence representation, implicitly treating structurally heterogeneous molecular components as equally difficult and equally important to reconstruct. However, different molecular graph token roles exhibit substantial variation in denoising difficulty and their influence on the decoded molecule, motivating role-specific corruption strategies. We introduce MotifRole-Diff, a role-aware corruption process that allocates masking rates according to empirically measured denoising difficulty and graph-level perturbation impact while preserving the model architecture, clean sequence space, and lossless molecular-graph decoder. We formulate schedule selection as the risk-optimal allocation of a fixed masking budget across token roles. Our theorem characterizes optimality for the modeled role-weighted residual risk, while downstream generation performance is evaluated empirically. Under matched architecture, training budget, and sampling compute, MotifRole-Diff improves validity on QM9 from 0.905 to 0.944 while reducing FCD from 1.701 to 1.609, and on MOSES improves validity from 0.920 to 0.938 while reducing FCD from 2.125 to 1.850. Role-wise diagnostics further show improved reconstruction across molecular graph token categories. Together, these matched-compute results indicate that structurally informed corruption is a more effective masking strategy than uniform schedules for serialized molecular graph diffusion.

Tasfia Nuzhat Ornee, Elias Hossain, Ivan Garibay +1

University of Central Florida

Masked Diffusion Models Molecular Graph Generation Molecular Generation Graph Diffusion

Jul 20, 2026cs.LG

One-step lowest-variance selection in a Gaussian random-field model motivated by masked diffusion: Total correlation and a square root collision threshold

Motivated by confidence-guided parallel unmasking in masked discrete diffusion, we study a single selection step in a stylized Gaussian random-field model. A locally dependent nonnegative score field represents position wise uncertainty, and the scheduler selects the K positions with the smallest scores. Dependence among the selected positions is measured through a distance-dependent Gaussian correlation model. This separation provides a tractable framework for quantifying how the geometry of low-score locations affects the dependence cost of factorized parallel decoding. We establish two complementary results. In a conservative sub-square-root regime, the conditional Gaussian total correlation of the selected block vanishes in probability. At the square-root scale, it remains non-negligible with positive asymptotic probability and admits a strictly positive expectation lower bound. Synthetic experiments support the predicted finite-size behavior. These results provide a rigorous stochastic-geometry baseline for understanding how budget size, score dependence, and spatial correlation jointly shape one-step confidence-based selection in masked discrete diffusion.

Linjun Li

Department of Mathematics, University of Pennsylvania, Philadelphia, PA.

Masked Diffusion Models Parallel Decoding Uncertainty Sampling Mutual Information

Jul 18, 2026cs.CL

Trace-Based On-Policy Distillation for Masked Diffusion Language Models

Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes \textbf{trace-based on-policy distillation (TOPD)}, a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4

\times

fewer rollout rounds, corresponding to an estimated 96.0

\times

to-accuracy model-compute speedup.

Haolin Ren, Ziyang Huang, Chenhao Yuan +2

Institute of Automation, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China

Masked Diffusion Models Diffusion Model Distillation Language Model Distillation Diffusion Language Models LLM Mathematical Reasoning Diffusion Language Model Distillation

Jul 17, 2026cs.CL

Induction in Both Directions: A Mechanistic Analysis of In-Context Learning in Masked Diffusion Language Models

While the internal mechanisms of autoregressive (AR) transformers have been studied extensively, much less is known about diffusion language models (DLMs), an emerging alternative that generates text by iterative denoising. In this work, we study how DLMs implement induction, a mechanism behind in-context learning in which the model finds a repeated context and copies the token that followed it. Our analysis compares attention-only AR models and absorbing-mask DLMs with matched architectures. We find that DLMs learn a bidirectional induction circuit, where previous-token and next-token heads write local context into the residual stream and later induction heads use it to find and copy the answer from the matching source position. The circuit is direction-symmetric, working whether the source appears in the past or in the future. When only left context is visible, matching what an AR model sees, the DLM does not outperform its AR counterpart in induction capabilities. However, we observe it has stronger induction when both sides of the masked token are visible, pointing to bidirectional context access rather than a stronger one-sided mechanism. Beyond induction, we provide causal evidence that DLMs compute the global fraction of masked tokens and use it as an implicit timestep, even though they are given no explicit timestep embedding.

Andy Catruna, Emilian Radoi

National University of Science and Technology POLITEHNICA Bucharest · Academy of Romanian Scientists

Masked Diffusion Models In-Context Learning Circuits in Language Models Induction Heads

Jul 17, 2026cs.CL

Adaptive Multi-Step Lookahead Decoding for Diffusion Language Models

Masked diffusion language models (DLMs) enable parallel text generation by iteratively refining masked tokens, offering a promising alternative to autoregressive decoding. Recent lookahead-based decoding methods improve the accuracy--efficiency trade-off by exploring future decoding states before committing token updates. However, existing approaches mainly rely on shallow one-step lookahead, which optimizes immediate information gain but can be suboptimal for longer-horizon decoding trajectories. Meanwhile, we find that a naive extension for deeper lookahead is also ineffective, as fixed-depth rollout introduces additional computation and cannot adapt to heterogeneous intermediate decoding states. Thus, in this work, we propose AdaLook, an adaptive lookahead framework for DLM decoding. AdaLook dynamically determines whether to continue rollout based on candidate-score variance and further enables branch expansion when intermediate rollout states require additional exploration. This design avoids unnecessary deep rollout while allowing the decoder to re-trigger lookahead from informative intermediate states. Experiments on various benchmarks and models demonstrate that AdaLook achieves a better accuracy--decoding steps trade-off than existing one-step lookahead decoding methods.

Yingqian Cui, Wei Deng, Lantao Mei +4

Michigan State University · Morgan Stanley · IBM T.J. Watson Research Center

Masked Diffusion Models Language Model Decoding Diffusion Language Model Decoding Diffusion Model Inference Acceleration

Jul 16, 2026cs.CL

Mask-Aware Policy Gradients for Diffusion Language Models

Reinforcement learning has proven effective for improving reasoning in large language models, but extending it to Masked Diffusion Language Models (MDLMs) remains challenging due to the intractability of the log-likelihood estimation. Existing approaches approximate this log-likelihood by modeling only the token predictions, ignoring the order in which positions are unmasked during generation. We observe that MDLM generation involves two decisions at each step: what tokens to place at each masked position and which positions to remask. We formalize this as a two-stage action MDP, showing that the policy gradient naturally decomposes into a token term and a masking term. Combining optimization of both terms leads to state-of-the-art outcomes on mathematical reasoning and coding benchmarks, with scores of 87.1% on GSM8K and 53.4% on MBPP.

Haran Raajesh, Kulin Shah, Adam Klivans +1

Department of Computer Science The University of Texas at Austin

Masked Diffusion Models RL for Language Model Reasoning Policy Gradient Methods RL for Diffusion Models

Jul 16, 2026cs.LG

A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models

We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC). We consider policy optimization problems and derive the corresponding policy gradient methods, leading to continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO). As a primary application, we develop a complete continuous-time RL framework for fine-tuning score-based discrete diffusion models. The proposed framework enables reward-driven optimization without requiring differentiability on the reward signals. In contrast to the existing GRPO-based approaches that only rely on terminal rewards, our formulation allows intermediate reward or advantage signals to be incorporated throughout the denoising trajectory. Importantly, when specialized to masked diffusion models (MDMs), our framework encompasses a rich class of policy parameterizations over the vocabulary simplex with analytically tractable probability ratios, providing a unified perspective on exploration and policy optimization in MDMs. For masked diffusion large language models (dLLMs), we further propose trajectory subsampling techniques to efficiently estimate computationally prohibitive trajectory likelihoods, reducing the computational cost of computing per-position probability ratios. We showcase the effectiveness of our methods on both low-dimensional entropy-regularized optimization problems and RL post-training of dLLMs on mathematical reasoning and coding tasks.

Zikun Zhang, Jiayuan Sheng, David D. Yao +1

Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027

Masked Diffusion Models RL for Language Model Reasoning Diffusion Model Fine-Tuning Continuous-Time RL RL for Diffusion Models Diffusion Language Models

Jul 15, 2026cs.LG

Discrete Diffusion Models: A Unified Framework from Tokenization to Generation

Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamentally shaped by how the discrete state space is constructed: the tokenization scheme, the vocabulary topology, and domain-specific structural alphabets. This work introduces a unified conceptual framework that views discrete diffusion models through the construction of the underlying discrete state space. Within this framework, existing formulations, including transition-matrix, masking/absorbing-state, and score/ratio-based approaches, emerge as different instantiations of a common design space. The framework further exposes common design trade-offs across training objectives, inference algorithms, scaling behavior, systems optimization, and evaluation protocols, suggesting several promising directions for future research.

Ye Yuan, Weien Li, Rui Song +19

McGill University · University of Cambridge · Mila - Quebec AI Institute +6

Masked Diffusion Models Diffusion Model Sampling Diffusion Models

Jul 14, 2026cs.LG

Concurrent Image Understanding and Generation: Self-Correcting Coupled Markov Jump Processes

Human cognition does not separate understanding and generation. A teacher at a whiteboard speaks and draws

\textit{together}

, each modality reshapes the other. In this paper, we bring this coupled loop to artificial systems. Masked Diffusion Models (MDMs) are ideally suited to this task, yet existing samplers either decode text and image interleavedly or independently update them in parallel branches that share only previous-step history, but not the other modality's latest decisions

\textit{within}

the same step; combined with MDMs' inability to remask, cross-modal contradictions are neither detected nor repaired. We introduce

\textbf{Self-Correcting Coupled Markov Jump Processes (SC-CMJP)}

, a framework in which one modality's transition rates are functionals of the other modality's confidence score, as weighted by cross-modal attention. Furthermore, a remasking jump retracts commitments the moment cross-modal evidence turns against them. In conjunction with SC-CMJP, we introduce

\texttt{CO}_\texttt{2}\texttt{Jump}

(Self-

\underline{\text{CO}}

rrecting

\underline{\text{CO}}

upled

\underline{\text{Jump}}

), a novel training-free single-pass sampler for joint multimodal geneneration. For training and evaluation purposes, we have created and will release three large-scale joint multimodal generation corpora:

\text{JEdit-1M}

,

\text{JMaze-200K}

,

\text{JNono-200K}

, with matching in- and out-of-distribution benchmarks.

\texttt{CO}_\texttt{2}\texttt{Jump}

achieves best joint performance for image understanding and editing as well as visual reasoning (maze and nonogram solving). The performance of the sampler scales monotonically with the number of denoising steps, evidence that the benefits of cross-modal coupling

\textit{compound}

across the trajectory. Project page: https://coupled-jump.github.io

Minh-Quan Le, Armand Comas, Alexandros Lattas +7

Google · Stony Brook University · Google DeepMind

Masked Diffusion Models Markov Models Cross-Modal Alignment Multimodal Generation Multimodal Learning

Jul 14, 2026cs.LG

Accelerating Masked Diffusion Large Language Models: A Survey of Efficient Inference Techniques

Diffusion large language models (dLLMs) offer a theoretical advantage in parallel generation over standard autoregressive models. However, parallel generation alone does not guarantee practical speedups. Realizing this efficiency requires specialized inference mechanisms, such as diffusion-aware caching and reuse. Consequently, as inference efficiency becomes a prerequisite for practical deployment, recent research has actively explored acceleration techniques across algorithms, architectures, and systems. However, rigorous comparisons remain difficult, as end-to-end latency stems from intricate trade-offs between algorithmic, architectural, and system-level factors that are often conflated in existing benchmarks. In this survey, we introduce a unified latency decomposition framework for dLLMs to disentangle these factors and analyze their impact on inference speed in real deployments. Guided by this framework, we categorize acceleration techniques along three axes covering algorithmic innovations, architectural and system optimizations, and inference-time scaling. Finally, we provide guidelines for reproducible benchmarking and highlight open challenges for realizing the full potential of parallel generation.

Daehoon Gwak, Minhyung Lee, Junwoo Park +1

KAIST AI · Yonsei University

Masked Diffusion Models Inference-Time Scaling Diffusion Language Model Inference Diffusion Language Model Decoding Diffusion Model Caching

Jul 12, 2026cs.LG

Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion

We introduce Sticky Jump Diffusions (SJDs), continuous-time Markov processes on

\mathbb R^d

whose discrete anchors are token embeddings. In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space; time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law. We estimate the score and the per-anchor reverse hazards from a single denoising classifier via Denoising Hazard Matching, the hazard analogue of denoising score matching, with simulation-free cross-entropy training. SJD recovers masked diffusion, continuous diffusion, and hybrid diffusion as limits. Its reversal explains features that each family treats as given: the mask of masked diffusion carries no evidence about the source token because the unsticking kernel of every anchor collapses to the same absorbing point; the terminal projection of continuous diffusion is required due to the absence of atoms in its forward marginal, without which flux balance yields no reverse jumps; and the update rules of hybrid diffusion (commit rate, destination, and drift) all follow from flux balance rather than from separate design. Beyond these limits, the unsticking kernel becomes a design space: a cross-position blending corrupts each position toward a blend of its neighbors' clean values or embeddings, turning dependency structure such as spatial locality or a constraint graph into an inductive bias of the corruption itself, and improves over the identity-kernel hybrid on CIFAR-10, Text8, and Sudoku.

Pascal Jutras-Dubé, Patrick Pynadath, Jeremy Lu +2

Department of Computer Science Purdue University · Department of Mathematics Purdue University

Masked Diffusion Models Stochastic Differential Equations Diffusion Models

Jul 9, 2026cs.AI

MobiDiff: Semantic-Aware Multi-Channel Discrete Diffusion for Human Mobility Data Generation

Human mobility data are essential for transportation optimization, urban planning, and resource allocation, yet real-world mobility data are costly to collect and difficult to share due to privacy concerns. Recent diffusion-based methods have shown promise in synthesizing realistic mobility patterns, but they typically rely on continuous or latent spatio-temporal traces, limiting their ability to natively model discrete semantic events with explicit region, activity, time, and interval structures. To address this issue, we introduce MobiDiff, an end-to-end discrete diffusion framework that efficiently generates mobility data by directly denoising multi-channel semantic skeletons, avoiding the costly interpolation, latent trace construction, and coarse-to-fine realization pipelines widely used in existing diffusion-based methods. Specifically, MobiDiff decomposes each human check-in event into spatial, activity, and temporal channels, and employs structured event-, group-, and channel-level masking to jointly capture trajectory-level mobility patterns and within-event dependencies. We evaluate generation fidelity, privacy-preserving, and efficiency on three large-scale real-world datasets from Atlanta, Boston, and Seattle. Results show that MobiDiff effectively preserves trajectory length and temporal interval distributions while remaining competitive across broader mobility statistics; it is also much faster than state-of-the-art methods, e.g., 5.3

\times

faster than GeoGen on average during inference. These findings suggest that discrete diffusion offers an interpretable and efficient framework for synthetic mobility data generation.

Rongchao Xu, Lin Jiang, Dahai Yu +5

Florida State University Tallahassee, Florida, USA · Rutgers University Piscataway, New Jersey, USA · University of California, Los Angeles Los Angeles, California, USA

Masked Diffusion Models Synthetic Data Generation Diffusion Models

Jul 4, 2026cs.LG

Tensor-Train Joint Modeling for Few-Step Discrete Diffusion

Discrete diffusion promises orders-of-magnitude faster generation than autoregressive (AR) models for sequential discrete data, yet its full potential of few-step generation has remained out of reach due to a fundamental structural limitation. The conditional-independence assumption underlying current discrete diffusion models introduces a systematic parallelization bias that compounds with the number of tokens unmasked per step, becoming severe in the few-step regime that fast generation requires. We address this with the first framework for explicit joint distribution modeling in discrete diffusion via tensor decomposition, which represents the conditional clean distribution as a low-rank tensor with controllable expressivity. The framework supports both Canonical Polyadic (CPD) and Tensor-Train (TTD) decompositions, and we identify a structural bias of TTD toward dependencies between nearby tokens, formalized through Oseledets' theorem relating TT-rank to unfolding-matrix rank, which is well-suited to sequential data such as natural language and line notations for molecular data. To enable efficient generation, we present an iterative marginal inference procedure with specialization for predetermined position schedules. Our framework integrates into pretrained MDMs through lightweight fine-tuning, yielding substantial improvements in few-step generation at a fraction of the cost of training from scratch.

Byoungkwon Kim, Minhyuk Sung

KAIST

Masked Diffusion Models Tensor Decomposition TT Decomposition Few-Step Diffusion Sampling Diffusion Models

Jun 30, 2026cs.CL

TAG-DLM: Diffusion Language Models for Text-Attributed Graph Learning

Text-attributed graphs (TAGs), where each node carries a natural language description, require models to jointly reason over text and graph topology. Existing approaches often handle the two modalities separately: graph neural networks operate on shallow text features, while hybrids of LLMs and graphs use the language model mainly as a text encoder and delegate structure learning to a separate graph module. We propose method that unifies textual reasoning and graph message passing within a masked diffusion language model, a language model with bidirectional attention and generative decoding. For each graph instance, method linearises a sampled local neighbourhood into a token sequence and injects graph structure through a topology attention mask, which realises message passing over the graph. Because the diffusion language model can both interpret and generate text, the method adapts to different tasks simply by changing the prompt, supporting node classification, link prediction, and cross-dataset transfer with no target-specific fine-tuning. Experiments show that method outperforms graph neural networks, graph transformers, and LLM-based baselines on all three TAG benchmarks across two tasks, improving over the strongest baseline by up to 3.9 points.

Lingjie Chen, Yuanchen Bei, Haobo Xu +3

UIUC · VISA

Masked Diffusion Models Link Prediction LLM Reasoning with Graphs Text-Attributed Graph Learning Diffusion Language Models Node Classification+1

Jun 29, 2026cs.CV

Nemotron-Labs-Diffusion-Image: Advancing Masked Discrete Diffusion for High-Resolution Image Synthesis

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.

Shufan Li, Greg Heinrich, Hanrong Ye +4

NVIDIA

Masked Diffusion Models T2I Diffusion Models Diffusion Models

Jun 27, 2026cs.CL

Masked Diffusion Decoding as $x$ -Prediction Flow

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, with no representation of partial belief in between. This all-or-nothing regime discards rich predictive information and forces premature, irrevocable commitments, leading to poor performance under a limited decoding budget. In this paper, we reinterpret mask prediction as clean-state prediction (

x

-prediction) and show that it can be used to induce a continuous flow in 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 continuous decoder reaches 97% of its performance on the HumanEval dataset with 25% of decoding budget.

Weitian Wang, Lianlei Shan, Shubham Rai +2

Robert Bosch GmbH, Germany · University of the Chinese Academy of Sciences, China · Ruhr University Bochum, Germany

Masked Diffusion Models Diffusion Language Model Decoding Diffusion Model Inference Acceleration

Jun 26, 2026cs.LG

VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing

Inference-time scaling is a promising paradigm to improve generative models, especially when outputs must satisfy structural constraints or optimize downstream rewards. We consider Masked Diffusion Model (MDM) and introduce MDM-VGB, a discrete diffusion sampler that augments unmasking generation with theoretically principled reward-guided remasking. Inspired by the recent success of the classical Jerrum-Sinclair backtracking Markov chain in reward-tilted generation, MDM-VGB extends the backtracking random walk from a fixed prefix tree to a masked-state graph, allowing tokens to be unmasked and remasked at arbitrary positions. The resulting sampler favors unmasking and remasking moves that lead to higher-value partial configurations, enabling both effective high-reward generation and efficient repair of low-reward samples. We prove that MDM-VGB is robust to process-verifier noise and achieves quadratic complexity, while popular test-time heuristics such as best-of-

N

can incur exponential complexity due to error accumulation. Our theoretical findings are corroborated by strong empirical performance, particularly on popular constraint-satisfaction and scientific benchmarks such as Sudoku and QM9.

Kijung Jeon, Thuy-Duong Vuong, Molei Tao

Georgia Tech · UCSD

Constrained Generative Modeling Masked Diffusion Models Controllable Text Generation Diffusion Sampling Inference-Time Scaling

Jun 26, 2026cs.CL

Masked Language Flow Models

Masked Diffusion Models (MDMs) promise fast, parallel language generation, but their reverse transition factorises across token positions -- an approximation that breaks down in the few-step sampling regime where parallel generation ought to provide the greatest efficiency gains. Flow Language Models (FLMs) sidestep this limitation by learning a continuous flow that transports noise toward clean sequences represented in Euclidean space, inducing a flow map that can be distilled for single-step generation. However, this makes complex tasks requiring multi-step reasoning problematic for FLMs, as FLMs are forced to decode every token during generation. To address this, we introduce Masked Language Flow Models (MLFMs), which incorporate masking into FLMs using a continuous stochastic interpolant to bridge partially masked and clean sequences. This design enables conditional generation via continuous flows and allows pretrained MDMs to be converted into MLFMs through a simple, lightweight adaptation. Leveraging this flexibility, we propose a novel sampler that alternates continuous denoising with the discrete unmasking of confident tokens to better support multi-step reasoning. We evaluate our approach on GSM8K and MT-Bench and find, for the first time, that flow-based language models can be scaled to solve downstream reasoning and instruction-following tasks.

Iskander Azangulov, Kianoosh Ashouritaklimi, Leo Zhang +2

Department of Statistics, University of Oxford

Masked Diffusion Models Instruction Following Language Modeling Flow-Based Generative Modeling

Jun 25, 2026cs.SE

Speculative Refinement: A Hybrid Autoregressive Diffusion Decoding Strategy and Its Behavior Across Benchmarks

How should we evaluate generation systems that combine autoregressive (AR) and diffusion decoding? We study this question through Speculative Refinement (SpecRef), a training-free hybrid method that warm-starts a masked diffusion language model from an AR draft using entropy-guided selective masking. Evaluating SpecRef across six benchmarks (HumanEval, MBPP, GSM8K, BBH, ARC-Challenge, HellaSwag) with three distinct evaluation protocols (execution-based pass@1, exact-match, log-likelihood scoring), we surface several findings relevant beyond our specific system: (1) code benchmarks conflate structural discovery with logical correctness: providing a syntactic scaffold lifts accuracy from near zero to over 20% without changing the model, indicating that much of the baseline failure is structural; (2) a refinement tension phenomenon where multi-stage correction degrades already-correct tokens, exposing benchmark saturation ceilings invisible to single-model evaluation; (3) log-likelihood and generative evaluation produce different model rankings for the same model pair, suggesting they measure different capabilities; (4) standard Python post-processing silently breaks code evaluation for non-AR generators. These observations apply to any multi-stage or non-autoregressive generation pipeline and point toward more diagnostic evaluation practices.

Aditi Gupta, Neel Mishra, Kushagra Trivedi +1

IIIT Hyderabad, India · Microsoft

Masked Diffusion Models Language Model Generation Evaluation Autoregressive Diffusion Diffusion Language Model Decoding Code Generation Evaluation

Jun 24, 2026cs.CL

Improved Large Language Diffusion Models

Modern large language models are predominantly trained with autoregressive factorization and causal attention. We present \emph{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.

Shen Nie, Qiyang Min, Shaoxuan Xu +7

Gaoling School of Artificial Intelligence, Renmin University of China · Beijing Key Laboratory of Research on Large Models and Intelligent Governance · Engineering Research Center of Next-Generation Intelligent Search and Recommendation, MOE +1

Language Model Pretraining Masked Diffusion Models LLM Fine-Tuning Diffusion Language Model Inference Diffusion Language Models

Jun 22, 2026cs.LG

Scheduling Thoughts: Learning the Order of Thought in Diffusion Language Models

Masked diffusion language models decode by iteratively unmasking tokens, where the unmasking order defines an "order of thought" that strongly influences generation quality yet is typically chosen heuristically. We derive a tractable upper bound on the sequential decoding mismatch, measured by the Kullback-Leibler divergence and expressed in terms of the model's pathwise log-likelihood, with tightness under sufficient model expressivity. This bound induces a dense self-aware reward over ordered trajectories, casting order selection as a principled policy optimization problem with a frozen denoiser. We instantiate this idea as Self-Aware Scheduling (SAS), which learns a lightweight order policy using Group Relative Policy Optimization and applies seamlessly to both any-order and semi-autoregressive decoding. On Sudoku with 1B MDM, SAS improves puzzle accuracy from 82.0% (best heuristic schedule) to 91.8%, and reaches 97.5% with second-stage fine-tuning along learned trajectories. On mathematical reasoning with LLaDA-8B, SAS improves pass@1 on GSM8K from 64% to 76% and on MBPP from 39.5% to 41%, consistently matching or exceeding heuristic schedules across generation lengths and block sizes. Project page: https://jimmyxu123.github.io/SAS

Jiawei Xu, Minghui Liu, Aakriti Agrawal +2

University of Maryland, College Park · University of California, Los Angeles.

Masked Diffusion Models Language Model Decoding LLM Inference Scheduling Diffusion Language Model Decoding RL for Diffusion Models Diffusion Language Models+1

Jun 22, 2026cs.LG

Walk fast but be careful: Understanding Parallel Sampling in Masked Diffusion

In this paper, we use random walks on graphs as a verifiable sandbox for studying parallel sampling strategies in masked diffusion models (MDMs). We train an MDM on random walk samples from a fixed graph. The graph and transition kernel are never shown to the model and serve as latent structure that is both controllable and enables evaluation. The framework provides a validity check for generated walks and a measure of distributional fidelity through the estimated transition kernel. Using simple graphs, we theoretically prove that parallel unmasking via widely used scores such as lowest entropy is not uniformly better than random parallel sampling; even with exact conditional probabilities, performance critically depends on the conditional dependence structure induced by the graph, a phenomenon difficult to isolate in benchmarks like Sudoku. We also develop training-free bisection samplers for MDMs, which take logarithmically many steps in the sequence length and are provably exact for random walks if the learned marginals are exact. Experiments on graph-walk tasks confirm that different parallel samplers perform better on different graph structures. Experiments on pretrained MDMs show that bisection-style samplers provide strong speed-quality tradeoffs on OpenWebText generation and reasoning benchmarks including GSM8K, MBPP, and HumanEval. Together, these results use graph walks to uncover conditional dependence as a key principle of parallel MDM sampling and translate this insight into efficient samplers that transfer to language generation and reasoning.

Vansh Bansal, Cholyeon Cho, Syamantak Kumar +2

UT Austin SDS · UT Austin CS · UT Austin ECE

Masked Diffusion Models Diffusion Sampling Few-Step Diffusion Sampling Diffusion Language Model Decoding

Jun 16, 2026cs.LG

Recursive Scaling in Masked Diffusion Models

Masked diffusion models (MDMs) generate sequences by iteratively refining a partially masked state and committing tokens in parallel. We introduce recursion in MDMs and propose new Recursive Masked Diffusion Models (R-MDMs), which apply a shared denoising transformer

L

times within each denoising step, adding recursive depth as an additional compute axis without increasing parameter count. Across structured generation tasks, recursive depth improves quality at fixed parameter budget, matches substantially larger non-recursive models at matched FLOPs, and can reduce the number of denoising steps needed to reach a target quality. We interpret these gains with a dependence--fidelity decomposition of parallel decoding error: recursion refines model marginals at a fixed masked state, whereas denoising steps change that state by committing tokens. Building on this analysis, we propose to treat decoding as a two-axis decision (how many loops to run and which tokens to commit) and show that entropy-guided adaptive rules improve the quality--compute frontier over fixed schedules, transferring across various tasks on Sudoku, Countdown, RNA, and executable math generation. Together, these results establish recursive depth as a practical, complementary test-time scaling mechanism for MDMs.

Alba Carballo-Castro, Julianna Piskorz, Paulius Rauba +2

LTS4, EPFL, Lausanne, Switzerland · University of Cambridge, Cambridge, UK.

Masked Diffusion Models Diffusion Model Sampling Diffusion Sampling Test-Time Scaling Diffusion Models