Diffusion Language Models

Diffusion language models, which generate text by denoising a token canvas bidirectionally instead of emitting tokens left to right, have become competitive with autoregressive (AR) generation. Medical foundation models, however, remain almost entirely autoregressive. We adapt a mixture-of-experts diffusion language model, DiffusionGemma-26B, and benchmark it against its same-size AR sibling Gemma-4-26B under an identical LoRA recipe on medical visual question answering datasets, scored by a verbosity-robust LLM judge. Diffusion matches or exceeds AR on all of them, and the finetuned model (3.8B active) is competitive with frontier vision-language models; its decoding is also 3.5-4.4x faster. Beyond this parity, the diffusion model offers a drafting capability AR lacks: any-order infill. Because the canvas is denoised bidirectionally, a radiologist can fix report fragments and have the model fill the text between them, an operation inherent to diffusion but not to autoregression, which is subpar at it. This suits real reports, which are often terse or inconsistent across clinicians and institutions.

Generative reasoning re-rankers achieve strong recommendation accuracy by emitting a chain-of-thought before re-ordering a candidate list, but they are slow at inference: an autoregressive (AR) decoder spends one sequential forward pass per reasoning token, and the reasoning trace far exceeds the ranking it produces. To reduce this cost, block-diffusion language models decode many positions in parallel over a few denoising steps and are substantially faster, yet naively converting an AR re-ranker into one opens two accuracy gaps: (1) a structural gap: answer positions are denoised in parallel and scored independently, so the decoder emits invalid rankings (duplicated, dropped, or out-of-set identifiers) that AR avoids through left-to-right masking; and (2) a distributional gap: fine-tuning the converted model on fixed teacher trajectories is off-policy relative to its own decoding at inference, leaving a residual accuracy gap. To close both gaps while keeping the speedup, we propose Diffusion-GR2, a recipe that converts our AR reasoning re-ranker (GR2) into a block-diffusion re-ranker. First, conversion fine-tuning (CFT) adapts the AR-initialized diffusion model to denoise the answer into a valid permutation on its own, without an external constrained decoder. Next, on-policy distillation (OPD) then supervises the model on its own decoded trajectories with dense per-token targets from the AR teacher. Finally, we apply a reinforcement-learning (RL) stage against a re-ranking reward on top of OPD's on-policy policy. Experiments on Amazon Beauty demonstrate that Diffusion-GR2 recovers to near-parity with the AR re-ranker, while block-parallel decoding raises decode throughput by $2.4$--$3.5\times$ at the model's reasoning output length. Ablations show that CFT recovers most of the conversion gap, and that on-policy distillation further closes it to the AR reference.

Continuous diffusion language models such as ELF report record-low generative perplexity (Gen-PPL). We find a catch: these models repeat far more than human text, and Gen-PPL rewards rather than penalizes that repetition, so its low scores overstate quality. Strip the repetition and ELF-B's Gen-PPL rises from $19.5$ to $27.7$; the smallest model even posts the best Gen-PPL because it repeats most. We trace the repetition to its source: a contractive attractor along a single direction in the self-conditioning feedback loop, the loop that feeds each step's clean estimate into the next. Because the failure is one-dimensional, a one-dimensional fix suffices, and we propose one. ACE (Attractor-Contrast-Escape) subtracts that single, label-free direction from the feedback at each step. Estimated once on the $105$M model, the direction cuts repetition to near the human level while keeping quality competitive, and transfers near-unchanged to the $342$M and $652$M models and across samplers; the same recipe recovers useful directions on other architectures. Since Gen-PPL itself rewards repetition, we instead measure the compute each fix needs to produce human-clean text, where ACE is $1.5$--$5\times$ cheaper.

Reinforcement learning for diffusion large language models (dLLMs) has largely moved to trajectory-aware methods. The current state of the art, TraceRL, holds that random masking is mismatched with the model's inference trajectory, and it reconstructs that trajectory during training by slicing each rollout into up to K/s trajectory-aligned training samples, a cost that grows with the block size K. We show that this mismatch can be mitigated without reconstructing the trajectory. Our method, SLIM-RL, bounds the commit risk of each rollout step with a tau-budget decoder, reducing aggregate commit risk in the training data. During optimization, SLIM-RL trains on these risk-controlled rollouts with a trace-free random-masking objective that adapts variance-reduction tools, combining sequence-level importance sampling, deterministic quadrature over masking levels under a mean-preserving, monotonically decreasing per-block mask schedule that we introduce. On SDAR-4B, SLIM-RL matches TraceRL's best MATH500 accuracy on only 0.46x its training samples at block size 16, improving over TraceRL by 6.32% on MATH500 and 11.05% on GSM8K under matched dynamic sampling. At block size 4, the 4B SLIM-RL surpasses the larger LLaDA-8B and Dream-7B dLLMs on math, exceeding LLaDA-8B by 10.76% on MATH500 while staying below the autoregressive Qwen2.5-7B. On code, it improves over TraceRL by 4.20% on MBPP and 3.65% on HumanEval. The tau-budget decoder transfers training-free across LLaDA, Dream, and SDAR. The source code is available at https://github.com/laolaorkkkkk/SLIM-RL .

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.

Deterministic few-step generation succeeds on continuous image latents but collapses to incoherent text on continuous text latents, and we show the cause is geometric rather than a training or scaling deficiency: a smooth, regularity-limited deterministic map cannot resolve a discrete branch choice before a sharp categorical readout, so few-step failure is governed by decoder sharpness, not transport accuracy. In the overlapping regime of real text autoencoders, we prove (Theorem 3) that the posterior-mean terminal step flips tokens at the rate of the latent mass in an $O(s(t))$ tube around decision boundaries. Two diagnostics, DABI (readout sharpness) and CCI (categorical commitment), measured on published checkpoints show that four independently built continuous-text decoders amplify a boundary-aligned perturbation far beyond a norm-matched isotropic one (DABI from $5\times10^{2}$ to $>10^{5}$), while image decoders have DABI $\approx 1$. Two mechanisms escape the continuous bound: categorical commitment (autoregressive decoders succeed despite sharper readouts) and stochastic re-injection (deterministic ODE at $K=4$ gives PPL 294 versus SDE 50 on the same model). In the idealized separated regime we prove matching sharp transport laws, including a dimension phase diagram: the deterministic stiffness needed to separate $M$ modes grows as $Θ(\sqrt{\log M})$ once the latent dimension is $Ω(\log M)$ (and as $M^{1/n}$ in fixed dimension), with a depth-$B$ hierarchy giving a $\sqrt{B}$-smaller per-step peak (Theorems 5-7); a coarea identity links these to the overlapping tube (Theorem 17). The result is an accuracy-depth-stiffness tradeoff: within the deterministic-continuous class the cost is irreducible, and both escapes step outside it.

Diffusion Language Models (DLMs) are typically trained under fixed context structures, restricting denoising to predetermined token subsets. This creates a mismatch between training and inference, where models must operate over arbitrary configurations, leading to degradation off the training grid. We propose Adaptive Block Diffusion (ABD), which resolves this mismatch by optimizing denoising risk over a distribution of prefix-window configurations. By treating the configuration as a stochastic variable, ABD trains a single model over the full configuration space without architectural changes. We show that generalization across decoding strategies is governed by the support of the training distribution, and that ABD guarantees denoising optimality for any inference policy whose configurations are covered during training. Empirically, ABD exhibits structural invariance across decoding scales, avoiding off-grid collapse and recovering a monotonic relationship between block size and perplexity, while matching or outperforming fixed-block specialists at their target scales.

Block Diffusion Language Models (BD-LMs) improve diffusion-based text generation with KV caching and flexible-length generation. A natural next step is to extend them from Single-Block Diffusion (SingleBD) to Multi-Block Diffusion (MultiBD), where a running-set of consecutive blocks is decoded concurrently for inter-block parallelism. However, existing BD-LMs are mostly trained under teacher forcing, where the model observes only one noisy block conditioned on a clean prefix. While the recent diffusion forcing strategy introduces visibility among multiple noisy blocks, its training states still differ from MultiBD inference, where decoding operates on a bounded running-set with heterogeneous slot-wise noise patterns. To bridge this gap, we propose Multi-Block Diffusion Language Models (MBD-LMs), obtained by post-training BD-LMs with Multi-block Teacher Forcing (MultiTF). MultiTF integrates teacher forcing and diffusion forcing by training on bounded noise-groups conditioned on clean prefixes, with randomized noise-schedulers that better match MultiBD inference states. To make MultiBD practically executable, we further introduce an optimized decoding algorithm based on the Block Buffer mechanism that preserves prefix-cache reuse, keeps input shapes static, and translates increased decoding parallelism into wall-clock acceleration. Empirically, MBD-LLaDA2-Mini increases average Tokens Per Forward pass (TPF) from 3.47 to 6.19 and improves average accuracy from 79.95% to 81.03%; when combined with DMax, MBD-LLaDA2-Mini-DMax reaches an average TPF of 9.34 with only a 1.02% accuracy drop on math and code benchmarks.

Diffusion language models (DLMs) have recently emerged as a promising alternative to conventional autoregressive language models. By generating multiple tokens in parallel during each denoising step, they offer higher inference throughput while maintaining competitive quality. However, realizing these throughput gains while meeting latency SLOs in a serving system requires addressing challenges introduced by DLMs' unique characteristics. These include navigating the speed-quality tradeoff created by confidence-based denoising, choosing appropriate parallelization levels across model instances under fluctuating load, and coordinating approximate KV caching mechanisms that introduce non-uniform per-step costs. To address these challenges, we present DiLaServe, a cluster-level serving system for DLMs. DiLaServe enables deadline-aware scheduling and adaptive load control through confidence-threshold adjustment, and dynamically reconfigures the cluster by solving a quality-aware optimization problem, while explicitly modeling the step-level heterogeneity introduced by approximate KV caching. Across multiple benchmarks and real-world traces, DiLaServe improves SLO attainment by up to 56.6 percentage points and reduces end-to-end request latency by up to 46% while incurring less than 1% accuracy drop.

Discrete diffusion language models (dLLMs) recover masked tokens in parallel, offering significant speedups over autoregressive (AR) generation. However, such promising frameworks face a fundamental architectural design dilemma: \ding{182} Adopting bidirectional attention achieves strong generation quality by allowing each position to access the full context, but is inherently incompatible with KV caching, limiting inference throughput in batch-serving scenarios; \ding{183} Conversely, causal attention enables efficient cached inference but loses all right-side context, substantially degrading generation quality. This paper introduces Bifocal dLLMs, a new paradigm that resolves this dilemma through asymmetric bidirectional context. Analogous to bifocal lenses, we instantiate the paradigm as R2LM (Right-to-Left Mamba), which combines two complementary mechanisms: $a$) standard causal attention providing precise left-context with full KV cache compatibility, while $b$) a lightweight reverse Mamba SSM sidecar supplying compressed right-side context without breaking cacheability. Comprehensive experiments on continued pretraining of Qwen3-1.7B with 60B tokens demonstrate that R2LM achieves $2.4\times$ to $12.9\times$ higher throughput than bidirectional dLLMs and $1.9\times$ to $2.9\times$ speedup over AR baselines in batch serving through parallel decoding with KV caching, while exceeding the causal baseline on most benchmarks and surpassing the bidirectional dLLM on average.

Diffusion language models offer a promising alternative to autoregressive models due to their potential for parallel and iterative generation. However, existing approaches use a single network for both context representation and iterative denoising, forcing one model to serve both roles and limiting its capacity for either role. We propose TwoTower, a block-wise autoregressive diffusion model that decouples these roles into two towers: a frozen AR context tower that causally processes clean tokens, and a trainable diffusion denoiser tower with bidirectional block attention that refines noisy blocks via cross-attention to the context. Built on Nemotron-3-Nano-30B-A3B, an open-weight 30B hybrid Mamba-Transformer MoE model, and trained on approximately 2.1T tokens, Nemotron-Labs-TwoTower retains 98.7% of the autoregressive baseline's quality while offering 2.42X higher wall-clock generation throughput. We release the code and model weights at https://huggingface.co/collections/nvidia/nemotron-labs-twotower.

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

Reinforcement learning (RL) has become a dominant post-training paradigm, driving the emergence of high-performance RL systems such as veRL for autoregressive large language models (LLMs). In parallel, diffusion-oriented RL algorithms, e.g., DanceGRPO and FlowGRPO, have rapidly expanded the scope of RL from language reasoning to diffusion-based visual and flow-based generation. However, efficient RL systems for diffusion generative LLMs remain underexplored. Existing implementations, e.g., veRL-Omni, still rely on colocated execution, which simplifies synchronization but couples rollout and training resources, limits heterogeneous deployment, and constrains independent scaling. To this end, we introduce DigenRL, a disaggregated RL framework for diffusion-based generative LLMs that supports flexible resource allocation, accommodates heterogeneous GPUs, and facilitates efficient task scheduling. To maximally reduce the execution bubbles in the disaggregated architecture, we propose: 1) a generation-axis pipeline (GAP) and time-step parallelism (TSP) in the diffusion architecture to enable finer-grained pipelining between rollout and training; 2) an elastic trainer-assisted generation (TAG) approach to enable the trainer GPU resources to dynamically assist in executing rollout generations; and 3) a tightly one-step constrained asynchronous strategy to further utilize the tail bubble in the pipeline. Extensive experiments are conducted on three hardware testbeds with 16-32 GPUs using HunyuanVideo-13B, Wan2.1-14B, FLUX.1-12B, and QwenImage-20B generative models. Experimental results show that DigenRL achieves 1.56-2.10x throughput improvements over state-of-the-art diffusion RL systems, veRL-Omni and GenRL.

Discrete diffusion language model (DLM) fine-tuning inherits inexpensive diagnostics from denoising-time confidence monitors, but their PEFT-training meaning is untested. We test top-1 argmax concentration as a collapse warning. Across 816 LoRA/PEFT configurations from three DLM families, the warning fires for every configuration while logs record 0/816 actual collapses at the 200 step horizon, giving zero precision. The cause is pre-equilibrium saturation: top-1 concentration is already high before optimization and quickly becomes insensitive to final training stability. We then evaluate max LoRA gradient norm, a parameter-side signal that samples gradient routing rather than token concentration. On a pooled held-out LLaDA-family split, a train-optimized threshold identifies top-decile final-loss configurations with precision 0.68 and F1=0.79, above the all-positive top-1 baseline even at the lower split-bootstrap confidence bound. Autoregressive controls and cross-family threshold failures bound the result to short-horizon DLM-LoRA inspection rather than a universal collapse detector. Workflow: drop top-1 as a PEFT alarm, log max-gradient early in training, and calibrate thresholds per DLM family before routing runs for inspection.

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

Standard tokenwise diffusion LMs keep training corruption and inference commitment at token granularity throughout denoising. At high noise, this leaves scattered local fragments rather than coherent evidence, making it hard to form early coarse structure, exactly what planning-sensitive generation requires. Hierarchical planning methods add coarse stages to separate planning from wording, but they need extra planners, block latents, or two stage designs. We propose Noise Dependent Granularity Control (NDGC), a single-level diffusion method that uses the noise level as a granularity cue. NDGC aligns training exposure and inference commitment with denoising progress. High noise steps use coherent token groups to support early meaning commitment, while low noise steps return to token level refinement. This creates planning like coarse to fine denoising without an explicit planner or hierarchical architecture. Across controlled tests, ablations, and WritingPrompts, NDGC shows earlier skeleton formation, better ordered recovery, and healthier outputs.

LLM reasoning transparency is a critical affordance for understanding model decisions, mitigating misuse and misalignment, and debugging surprising model behaviors. However, DiffusionGemma performs a larger fraction of its computation in a continuous latent space; does this make its reasoning less transparent? We study this question by decomposing transparency into two components: variable transparency, whether we understand intermediate snapshots of a model's computational state; and algorithmic transparency, whether we can use these snapshots to reconstruct the process by which the model arrived at its outputs. Naively, DiffusionGemma has poor variable transparency: its opaque serial depth, the amount of serial computation that occurs in between interpretable model states, seems at first 28.6X higher than the corresponding autoregressive Gemma 4 model. However, we show that we can map the information flowing between denoising steps through an interpretable token bottleneck with no decrease in downstream performance. Treating these intermediate states as interpretable reduces the opaque serial depth to just 1.1X that of Gemma 4. Algorithmic transparency is harder for diffusion models than for autoregressive models because all token predictions in the canvas can change at every denoising step, giving the model the power to implement complicated distributed algorithms during the denoising process. To begin bridging this gap, we conduct a suite of interpretability case studies, uncovering initial evidence of novel diffusion-specific phenomena such as non-chronological reasoning, token and sequence smearing, and intermediate-context reasoning. Finally, we test monitorability, a key application of transparency that measures whether model outputs are useful for downstream tasks. We find that DiffusionGemma is similarly monitorable to Gemma 4.

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

Enhancing the formal math reasoning capabilities of Large Language Models (LLMs) has become a key focus in both mathematical and computer science communities in recent years. While significant progress has been made in using state-of-the-art Auto-Regressive (AR) LLMs for formal theorem proving, these models suffer from inherent limitations. Their next-token prediction generation methods may yield suboptimal performance due to the challenges of long-range coherence and the compounding of errors over long sequences. Recent advancements in diffusion LLMs (dLLMs), which generate text through iterative denoising of a multi-token block, offer a promising alternative. However, the application of dLLMs to formal mathematics, where maintaining long-range coherence is critical, remains largely understudied. To address the challenges above, we propose Diffusion-Proof, to the best of our knowledge, the first framework to train and apply dLLMs for formal theorem proving. Our frameworks contain training and inference methods for two models. The first one is dLLM-Prover-7B, which performs whole-proof writing with long-range coherent tactic usage. The second one is dLLM-Corrector-7B, which is a novel large block diffusion-based correction model. It leverages the in-filling capabilities of dLLMs to perform local proof correction using bi-directional information. Extensive experiments demonstrate that Diffusion-Proof relatively significantly outperforms the AR LLM baseline trained under the same dataset. Diffusion-Proof achieves an absolute improvement of 1.61% on ProofNet-Test and 6.14% on MiniF2F-Test benchmarks compare to the baseline. Notably, Diffusion-Proof successfully resolves one IMO problem that more advanced thinking model DeepSeek-Prover-V2-7B could not solve, showcasing the unique advantage of dLLMs in formal theorem proving.

Block diffusion language models accelerate decoding through parallel block-wise denoising, yet whether they can be reliably scaled for long chain-of-thought (CoT) reasoning remains unresolved. To this end, we develop DreamReasoner-8B, an open-source block diffusion reasoning model, and conduct a systematic study of how training and inference block sizes affect long-CoT reasoning. Our analysis reveals a stark performance disparity: training with large block sizes yields remarkably poor reasoning, whereas small block sizes preserve effective reasoning. To bridge this granularity gap, we propose block-size curriculum learning, which gradually transitions training from fine-grained to coarse-grained block sizes, thereby overcoming this limitation and enabling strong reasoning performance that generalizes across diverse inference block sizes. On mathematical and code reasoning benchmarks, DreamReasoner-8B achieves results competitive with leading open autoregressive models such as Qwen3-8B. This work establishes a practical foundation for efficient, reasoning-capable diffusion language models. We release our model at https://github.com/DreamLM/DreamReasoner.

Diffusion models have become a promising alternative to autoregressive models. Among these, uniform diffusion language models (UDLMs) permit any token to be updated at any step, in principle enabling more flexible generation. However, no UDLM has yet been pretrained from scratch at both large parameter scale and large token budget. Both autoregressive modeling and masked diffusion modeling already have capable models at scale that the community can study and build on; uniform diffusion has none. A scratch-pretrained UDLM at scale would provide a clean reference point for studying scaling behavior, generation dynamics, controllability, and trade-offs against established autoregressive and masked diffusion models. To this end, we introduce Sumi ("ink" in Japanese), a fully open 7B uniform diffusion language model pretrained from scratch on 1.5T tokens. Sumi performs competitively with autoregressive models trained at comparable token budgets on knowledge, reasoning, and coding benchmarks, while under-performing on commonsense benchmarks, where our education-heavy data mixture is a likely contributor. We release our model weights, checkpoints, and full training recipe, including a complete specification of the data mixture over publicly available corpora. We hope this release enables the community to study native uniform diffusion at scale and catalyzes work on its as-yet poorly understood aspects.

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

MDLMs generate text by denoising a preallocated masked response canvas, making response-length modeling central to instruction tuning. Existing MDLMs often inherit the autoregressive convention of using repeated [EOS] tokens for padding during instruction tuning, giving [EOS] a dual role as both a semantic terminator and a padding token. We show that this dual role is a root cause of [EOS] overflow under large-block decoding. To decouple these roles, we propose VoidPadding, which introduces [VOID] for padding and reserves [EOS] for termination. During inference, the learned [EOS] signal enables early stopping, while the learned [VOID] signal guides adaptive response canvas expansion. On Dream-7B-Instruct, VoidPadding improves the block-size-averaged four-task mean across mathematical reasoning and code generation benchmarks by $+17.84$ points over the original model and $+6.95$ points over RainbowPadding, while reducing decoding NFE by 55.7% on average. Code is available at https://github.com/Haru-LCY/VoidPadding.

Token-to-token (T2T) editing lets LLaDA2.1 revise committed tokens during block-diffusion decoding. The released recipe trains this editor on random vocabulary corruptions, but at inference the editor sees the model's own fluent, high-confidence draft errors instead. We study this training-inference mismatch and propose self-generated T2T, which performs a no-gradient draft pass, fills masked positions with predicted tokens, and supervises recovery in a second pass under these self-generated corruptions. We implement the update as a short LoRA continued-pretraining pass on LLaDA2.1-mini and evaluate on several benchmarks under the official Q-Mode T2T procedure with unchanged inference parameters. The method generally improves accuracy while reducing T2T edit intensity, mitigating failure modes such as final-digit transcription errors after otherwise correct reasoning and excessive self-correction before short factual answers.

Diffusion large language models (dLLMs) offer a promising alternative to autoregressive decoding by iteratively refining masked sequences, enabling parallel token updates and bidirectional conditioning. Their practical efficiency, however, is limited by sampling procedures that execute a fixed number of reverse denoising steps selected before decoding, spending computation on already-stable positions and sometimes committing unstable ones too early. We present LESS, a training-free, model-agnostic adaptive sampler that treats token commitment as an online stopping problem. LESS implements mutual-stability sampling through a joint stability rule that makes a masked position eligible for unmasking only when its top-1 prediction has high confidence, its top-1 token persists across recent reverse steps, and its predictive distribution is stable under top-$K$ inter-step Jensen--Shannon divergence. We evaluate LESS on Dream-7B, LLaDA-8B, and LLaDA-1.5-8B, covering full-sequence diffusion and semi-autoregressive blockwise sampling regimes, across seven benchmarks spanning general knowledge, math, and code. LESS improves average accuracy over strong training-free adaptive samplers while using $72.1\%$ fewer reverse steps than fixed-budget decoding. Since each reverse step requires a Transformer forward pass, these step-count reductions translate into fewer forward evaluations, lower measured wall-clock latency, and lower estimated inference compute.

Diffusion Large Language Models (dLLMs) offer a promising avenue for parallel generation but face a trade-off between decoding speed and quality. While revocable decoding strategies attempt to mitigate errors by verifying and remasking tokens, they typically operate within a mixed-quality context. This leads to two critical failures: Error Propagation, where new tokens absorb toxic information from erroneous context, and Local Error Reinforcement, where errors mutually reinforce each other to evade detection. To alleviate these challenges, we propose ASRD (Anchor Supervised Revocable Decoding), a training-free framework that operates within the embedding space. ASRD explicitly decouples the decoding context into trusted Anchor Tokens, which are identified via temporal consistency, and uncertain candidates. Leveraging a dynamic Anchor Tokens Cache, we introduce two complementary mechanisms: (1) Anchor-Guided Generation, which injects entropy-weighted anchor signals into masked positions to implicitly rectify attention toward the reliable global skeleton; and (2) Anchor-Perturbed Verification, which applies orthogonal perturbations to uncertain candidate tokens, destabilizing and remasking errors driven by fragile local consensus. Extensive experiments on math and coding benchmarks demonstrate that ASRD outperforms recent remasking baselines, achieving accuracy improvements of up to 6.4% while accelerating inference throughput by up to 7.2$\times$.The code is available at https://github.com/preordinary/ASRD.

While reasoning on autoregressive (AR) models is often performed by chain-of-thought reasoning and reflection, their refinement of previous outputs still relies on fully sequential generation, even when only local edits are needed. In contrast, the masking mechanism in Mask Diffusion Models (MDMs) naturally supports explicit local edits on previous outputs, allowing selective refinement without discarding previous answers and generating another from scratch. While this property more closely aligns with how humans correct mistakes by iterative local refinement, existing MDMs do not support multi-turn masking and denoising. We propose Reflective Masking (RM), which elicits such an intrinsic reasoning capability in MDMs via lightweight post-training. RM provides a native test-time scaling, where an MDM iteratively revisits and revises its prior outputs based on evolving context. To exploit insights from previous turns like AR reasoning, we further introduce History Reference, a parameter-free mechanism that leverages intermediate denoising states during revision. Our approach requires no architectural changes and is easily applicable to existing MDMs. Across diverse tasks and modalities, including text generation, Sudoku, and image editing, Reflective Masking consistently outperforms standard masking-based baselines and demonstrates strong generality, positioning RM as a fundamental primitive for reasoning on MDMs.

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

Discrete diffusion language models enable parallel token generation, offering a pathway to low-latency decoding. However, selecting tokens independently by marginal confidence limits effective parallelism: tokens that appear reliable in isolation can form incompatible configurations when several positions are updated at once. We introduce a training-free decoding framework that coordinates these parallel updates. At each forward pass, the method assigns a commit score to each masked position and refines these scores using pairwise interactions derived from the model's predictive distributions. A variational relaxation yields a simple fixed-point update that suppresses conflicting simultaneous commitments within a single forward pass. This mechanism allows the decoder to commit more tokens in parallel while maintaining competitive generation quality. The method is lightweight, requires no auxiliary model or retraining, and drops into existing diffusion decoding pipelines without modification. Experiments on reasoning and code-generation benchmarks show consistent improvements in the quality-latency trade-off.

Diffusion Language Models (DLMs) have demonstrated strong scaling capacity as alternatives to autoregressive language models. However, their performance is highly sensitive to the choice of transition kernels, and poorly designed kernels can lead to issues like training instability, slow convergence, and biased sampling. In this paper, we study this sensitivity through a principled analysis of generalization error and identify three critical factors: asymptotic bias (difficulty in approximating the posterior distribution), exposure bias (error propagation during sampling), and optimization variance induced by kernel dispersion. We further compare different transition kernels: masking diffusion yields sparse and easier posterior-approximation targets, while uniform diffusion provides stronger sampling-side repair but induces harder approximation. Motivated by this trade-off, we revisit a previously overlooked variant, semantic DLM (SemDLM), where the transition kernel corrupts tokens to neighborhoods that are semantically similar. Our theory suggests that SemDLM can serve as a plausible middle ground by reducing the posterior approximation difficulty of uniform diffusion while retaining repair ability. However, we find that SemDLM suffers from a semantic basin problem, where sampling repeatedly stays within a semantic region and produces low-diversity text. To address this, we propose SemDLM+, which adds a global transition and a semantic-frequency penalty during sampling. Experiments on LM1B and OpenWebText show that SemDLM+ improves training dynamics and achieves competitive language modeling and generation quality with satisfactory diversity.