Masked Diffusion Language Models

Masked diffusion language models (dLLMs) generate text by iteratively denoising masked tokens with bidirectional attention. Extending reasoning across generation chunks normally requires keeping earlier generated text in context. We ask whether a dLLM can instead continue reasoning after that text is cleared, using only a fixed-size carried state. We implement this state as a small number of register tokens: dedicated fixed-position tokens whose continuous hidden states are trained to carry reasoning progress across generation chunks. We post-train dLLMs to decode a chunk of text, clear it while preserving the register values, and continue decoding from the prompt and carried state. In our main comparisons on LLaDA and Dream, registers outperform discrete-text carry on every benchmark, with gains of up to 8.5 points on math and 19.5 points on code. Registers are especially effective for bounded code generation, where correct programs usually span several chunks. Finally, registers can be further refined with reinforcement learning on long-horizon reasoning tasks.

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.

Antibody-specific language models pretrained via masked language modeling (MLM) learn representations that are critical for downstream sequence design and property prediction tasks. Yet, the corruption process itself is rarely leveraged as a source of inductive bias during pretraining. While preferentially masking complementarity-determining regions (CDRs) improves binding-related predictions, antibodies possess diverse biological priors over a variety of functions. Herein, we introduce function-aware masking, a family of pretraining algorithms that align mask placement with specific functional priors (e.g., from IMGT annotations or structure predictions) to shape the learned representation space. We show that these specialist masking strategies significantly improve performance on their respective objectives, yielding up to a 14% gain on structure-related tasks and up to a 5.9x improvement on CDR-related tasks. To further improve performance across multiple functional axes, we develop hybrid masking strategies that integrate multiple priors, balancing reconstruction over binding, structural, and biophysical objectives. Our results demonstrate that informed mask placement provides a parameter-free mechanism for imposing functional inductive biases in antibody language model training.

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.

Classifier-free guidance (CFG) is usually kept on throughout masked diffusion language model decoding, although its benefit varies across prompts and over time. We study when CFG is actually needed by comparing, from any partial output, the probability of eventual constraint satisfaction under continued CFG and under base-only continuation. Their difference defines the remaining value of guidance. Guidance dependence is highly prompt-specific. Many prompts already succeed without CFG, while for others it provides no measurable benefit or can be harmful. For prompts that do benefit, the gain is often concentrated early. We define the commitment horizon $\astar$ as the earliest point from which switching all remaining decoding to the base model reduces final success by no more than a chosen tolerance. Under the base model, the corresponding success probability, or committor, is a martingale. To first order, CFG's per-step effect is governed by the covariance between the guidance logit direction and the successor committor. This gives a local account of when guidance can help, but it does not by itself locate the horizon. Among prompts with an observed preterminal horizon, $\astar$ is usually early and varies more within constraint families than between them. Freezing each prompt at its own cross-fitted horizon is noninferior to full CFG on all 13 subtasks at the prespecified margin, even while many tokens remain masked. This separates commitment from realization. The boundary also identifies a later region in which higher parallelism adds only a small cost in constraint success, although fluency still degrades with parallel width. For failed trajectories, reopening committed positions improves recovery in both failure modes.

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.

Masked diffusion language models (dLLMs) can commit tokens in any order -- a freedom marketed as their core advantage over autoregressive decoding. We show that on reasoning tasks this freedom is instead the axis of failure. Logging every commitment during decoding of LLaDA-8B on GSM8K, we find that unconstrained (pure) decoding commits the final answer at 15-24% of the trajectory while half the reasoning region is still masked, and collapses to answer-only outputs on up to 90% of problems as the canvas grows. The cause is not the model's termination beliefs -- EOS "pressure" is nearly identical across decoders -- but reachability: whether the sampler may act on those beliefs at distant positions. A 2x2 prompt-decoder design shows that chain-of-thought helps only under ordered commitment (interaction +34.8 percentage points, 95% CI [26.8, 42.8]; without reasoning text the decoders are indistinguishable), an interaction we decompose into a collapse channel and an order channel and replicate on Dream-7B and MATH-500. A single-knob intervention -- frontier-gated commitment -- causally recovers the full gap (0.528 to 0.852) while preserving up to 4x parallel decoding, along a measured frontier whose optimal window flips from w=1 at full refinement to unconstrained at 8 tokens/step. Our results reframe existing window-style samplers, previously motivated by efficiency, as the minimal fix for a reasoning pathology they were never designed to address.

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.

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.

Industrial anomaly detection and localization are limited by scarce real anomalies and pixel-level annotations, a bottleneck that synthetic image-mask pairs can alleviate. However, existing few-shot mask-guided generation may over-follow mask geometry, produce weak anomalies, or use condition masks incompatible with the current object instance. We propose OSAGEN, which combines object-aware mask priors with multistage decoupled diffusion. Its three-stage adaptation sequentially learns normal appearance, defect appearance under coarse conditions, and fine-grained mask calibration, improving defect realization and local control. QBG injects object structure from a matched normal image into mask diffusion to produce object-aware priors, while ISC restricts anomaly propagation and preserves normal content during sampling. A lightweight materialization step recovers pixel-level labels aligned with the realized defects. On MVTec AD and VisA, OSAGEN achieves AP-P/F1-P scores of 88.1/82.2 and 68.5/66.1, respectively, under a unified downstream localization protocol. The code will be released upon acceptance.

Discrete diffusion and flow-matching models denoise a sequence over many steps, but to keep each step cheap, they factorize the transition across positions and decide every token independently. This makes few-step generation challenging for text when the target couples two positions, such as a subject and a verb that must agree. An independent update commits to them separately, and many function evaluations are spent repairing the mismatch. Existing few-step methods buy back the lost correlation by distilling or rectifying a slow teacher, and so inherit the teacher's quality ceiling. We ask instead whether a model can express correlated steps natively, and answer with Latent-Kernel Discrete Flow Maps (LKF), a from-scratch flow-map kernel that is a mixture of M factorized components tied by a single shared latent. Conditioned on the latent, each component is cheap, and the mixture is summed over the latent in closed form for small M. We show that a single step places mass on correlated completions with the same sampling time complexity as a factorized model, since one latent is drawn per sequence and reused across the entire denoising trajectory. We also show that the Masked Diffusion Language Model (MDLM) is a special case of our LKF model at M=1. The experiments for unconditional text generation on the One-Billion-Word (LM1B) and WikiText-103 benchmarks show that our LKF model learns strongly heterogeneous components and improves generative perplexity by 2.1x to 3.3x over the likelihood baselines without losing diversity. The gain grows with M, and at M=8, it surpasses distilled and rectified few-step samplers. The source code is available at: https://github.com/mansoor181/lkf.git

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.

Autoregressive (AR) large language models (LLMs) are inherently inefficient at inference time because each generated token requires accessing the full set of model parameters, leading to low operational intensity and high energy consumption. Masked diffusion language models (MDLMs) partially address this limitation for memory-bound settings by allowing multiple tokens to be generated per parameter access. In order to further enhance inference efficiency on modern platforms with extensive in-chip memory, this work proposes neuromorphic MDLMs (N-MDLMs), which integrate block diffusion with spike-based neuromorphic computation to jointly improve throughput and energy efficiency. While block diffusion increases token throughput by producing multiple tokens per parameter access, spike-induced sparsity reduces effective parameter traffic and computations by skipping inactive channels. To analyze the synergistic effect of sparsity and diffusion, we develop a token-level roofline-inspired model that captures the combined impact of block-parallel generation and spike sparsity on decoding efficiency. Experimental results on translation tasks show that, thanks to spike-induced sparsity, N-MDLMs achieve substantial improvements in energy efficiency and throughput even in compute-bound platforms for which MDLMs would fail to improve over AR-LLMs.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

Non-autoregressive generation offers a powerful paradigm for iterative refinement, allowing models to recursively critique, erase and regenerate arbitrary subsets of tokens. However, existing non-autoregressive models fail to realize this potential. Masked Diffusion Models (MDMs) suffer from factorization error, causing sample quality to collapse when generating multiple tokens simultaneously. Flow Map Language Models (FMLMs) circumvent this bottleneck via joint sequence transport for excellent few-step generation, but sacrifice the inference-time flexibility of MDMs. We introduce FMLM+, a framework that bridges this gap by equipping FMLM with masking-style noise schedules. While generating the full sequence in a single step, FMLM+ simultaneously scores the global consistency of each token a posteriori. We leverage this to introduce Posterior Refinement, a novel inference-time refinement strategy that enables the model to adaptively self-correct its outputs, matching the performance of discrete baselines with 32x fewer NFEs. Across diverse benchmarks, we demonstrate that FMLM+ with Posterior Refinement improves the speed--quality tradeoff over both MDM and FMLM families, providing a scalable foundation for high-fidelity language modeling.

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

In this paper, we propose using random walks on graphs as a verifiable sandbox to study different parallel sampling strategies in masked diffusion models (MDMs). We train an MDM on random walk samples from a fixed graph. The graph or the transition kernel is never shown to the model explicitly and plays the role of latent structure in the sequences, albeit one that is controllable and can be used for quantitative evaluation. Thus, this framework enjoys a Sudoku-like validity check: verifying that an output is a valid walk and estimating the Markov kernel from the walks to measure distribution fidelity. Using simple graphs, we theoretically prove that parallel unmasking via widely used scores like lowest entropy is not uniformly better than a random parallel sampler; the performance critically depends on the structure of the underlying graph. We develop a new bisection sampler for random walks, which takes logarithmic steps in the sequence length and is provably exact under perfect training. Experiments on various graph walk tasks show that different parallel samplers are better for different graphs even in practice. Our initial experiments on a pretrained OpenWebText MDM show that the bisection-style samplers improve speed-quality tradeoffs even for language generation. Together, these results position graph random walks as a mechanistic benchmark for diagnosing and designing parallel samplers for masked diffusion models.

Masked diffusion models (MDMs) have recently emerged as a promising paradigm for sequence generation. Scaling MDMs is conventionally achieved by increasing the parameter count or the number of denoising steps. We introduce Recursive Masked Diffusion Models (R-MDMs), which add recursive depth as a third scaling axis by repeatedly applying the same denoising transformer within each diffusion step. Recursion enables iterative refinement of the output through parameter reuse, increasing effective model depth without increasing parameter count. Across structured generation tasks, including Sudoku and Countdown, we show that R-MDMs achieve substantially improved parameter efficiency: a model with $L$ recursive iterations often matches the performance of non-recursive baselines with roughly $L\times$ more parameters. Moreover, recursive refinement can partially substitute for additional denoising steps, allowing recursive models to reach the same generation quality with fewer forward passes at inference time. These results suggest that recursive depth is a practically useful scaling mechanism for MDMs, improving both parameter efficiency and the allocation of test-time compute.

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 \texttt{[EOS]} tokens for padding during instruction tuning, giving \texttt{[EOS]} a dual role as both a semantic terminator and a padding token. We show that this dual role is a root cause of \texttt{[EOS]} overflow under large-block decoding. To decouple these roles, we propose VoidPadding, which introduces \texttt{[VOID]} for padding and reserves \texttt{[EOS]} for termination. During inference, the learned \texttt{[EOS]} signal enables early stopping, while the learned \texttt{[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.

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.

Masked diffusion language models (MDLMs) such as LLaDA now rival autoregressive (AR) LLMs, but every existing knowledge-editing and unlearning method (ROME, MEMIT, etc.) targets AR transformers and either makes assumptions that fail under iterative denoising, or requires gradient updates whose backward-pass activations cost tens of GB of extra VRAM and which collapse MDLMs at standard learning rates. We introduce TimeROME-DLM, the first training-free, gradient-free, inference-time knowledge-editing framework for MDLMs. It couples two components: a Temporal Indirect Effect (TIE) causal-tracing protocol that identifies, for each fact, the coordinate whose intervention most strongly drives the object prediction at later denoising steps; and a closed-form, low-rank residual edit memory that aggregates subject keys and target deltas across all forget facts and applies a single ridge-regularised update at that coordinate at every diffusion forward, with sparsification to limit utility spillover. Backbone weights stay frozen; only three hyperparameters (alpha, lambda, q) are tuned on a small validation split. On TOFU forget01 with TOFU-finetuned LLaDA-8B-Base, TimeROME-DLM cuts forget-set log-probability by roughly 83 nats. The same configuration transfers to LLaDA-8B-Instruct, Dream-7B, MMaDA-8B, DiffuLLaMA-7B, and LLaDA-MoE-1.4B. It keeps retain-set log-probability nearly flat (within ~1 nat at the utility-safe operating point) across 50 sequentially inserted facts, delivers a four- to fourteen-fold wall-clock speedup with zero additional VRAM over the strongest converged training-time baseline, and scales sub-linearly to 400 facts. TimeROME-DLM closes the locate-then-edit gap between AR LLMs and MDLMs at a fraction of the computational cost.

Summaries of real-world events can become outdated as contexts evolve and new information arrives. A common response is to generate a new summary from the updated context, but full regeneration discards the previous draft, can obscure what changed, and may be unnecessary when only a few claims are unsupported. We study localized faithfulness repair: updating outdated spans in an existing summary while preserving supported content. We propose DETECT-REMASK-REPAIR, a diffusion-based framework that identifies, remasks, and repairs outdated regions with masked diffusion language models. To evaluate evolving-context summarization, we introduce StreamSum, a benchmark of synthetic event timelines. Experiments on DialogSum and StreamSum show that localized diffusion repair provides a controllable alternative to full rewriting: faithfulness-steered repair improves early drafts, one-step repair reduces repair cost to under half a second, with the framework enabling faithfulness-speed-preservation tradeoffs across datasets. We also find that the framework can provide a post-hoc correction step that improves faithfulness for autoregressive systems.

Masked diffusion language models (dLLMs) have recently emerged as a competitive alternative to autoregressive language models, with the promise of faster inference via parallel token generation. A notable limitation of the masked formulation, however, is that once a token has been unmasked it can no longer be revised, leaving dLLMs vulnerable to early sampling mistakes. To address this, a growing body of work has sought to extend masked dLLMs with self-correcting (remasking) capabilities. One appealing subset of these methods does so in a training-free, post-hoc manner based on token confidences, with encouraging early reported results. In this work, we revisit the empirical evaluation of a representative post-hoc remasking method, WINO [Hong et al., 2026], and find that under standard decoding settings (shorter block lengths) it brings little-to-no benefit over confidence-based unmasking alone [Wu et al., 2025]. Extending the evaluation to non-greedy decoding, we find that while confidence-based remasking can mitigate errors introduced by increased stochasticity to some extent, it also exacerbates the diversity collapse previously reported for confidence-based unmasking. Overall, our results show that the benefits of post-hoc confidence-based remasking are highly setting-dependent, underscoring the need for a more comprehensive evaluation framework.

Masked diffusion language models can reduce inference steps by revealing multiple tokens per denoising iteration, but this parallelism is fragile: positions that are individually confident may be unsafe to commit together when their predictions are coupled. Existing training-free samplers such as Top-$k$, Fast-dLLM, and EB-Sampler mainly control how many tokens to reveal, while often ranking candidates by token-wise scores that ignore interactions within the selected set. We propose ADAS, a training-free reranking rule that leaves the base sampler's stopping rule unchanged and greedily discounts each token-wise confidence score according to its attention to already selected positions, weighted by their prediction uncertainty. Across LLaDA-8B-Base and Dream-7B-Base on the reasoning benchmarks GSM8K and MATH500 and the code benchmarks HumanEval and MBPP, plugging ADAS into all three samplers improves low-NFE performance at matched denoiser evaluations by $9.11$ and $10.46$ percentage points on average, respectively, with $3.1\%$ per-forward runtime overhead. Code is available at https://github.com/yusufsahin99/ADAS.

Masked diffusion language models generate text by iteratively unmasking many tokens in parallel, but this speed comes with a correction problem: tokens generated in the same step are predicted from marginal distributions, and early local dependency errors can later contaminate the context. PRISM addresses this by learning token-level quality scores and remasking unreliable tokens, but its inference rule is coupled: the same forward pass both detects low-quality tokens and computes logits for their replacements, so the erroneous tokens still condition regeneration. We propose NAVIRA, an inference-time decoding policy that separates these two operations and samples remasking positions stochastically. A first forward pass scores tokens; selected tokens are masked; a second forward pass regenerates from the cleaned context. Temperature-controlled remasking reduces repeated correction of the same positions and balances fluency against diversity. In controlled experiments with a 170M masked diffusion language model, decoupling improves fluency, while scheduled stochastic remasking preserves entropy and achieves stronger LLM-judge scores under larger forward-pass budgets. These results show that remasking policy, not only the learned quality signal, is central to reliable masked-diffusion text generation.

Knowledge editing aims to update or correct factual knowledge in a language model. A widely used approach, locate-then-edit, first localizes a fact within the model and then edits the weights there. To date, such methods have been developed exclusively for autoregressive models (ARMs). Whether they work for masked diffusion models (MDMs), which model text bidirectionally and generate by iterative denoising rather than next-token prediction, remains an open question. We address it by transferring locate-then-edit to MDMs and comparing multiple MDMs with their matched ARMs. Our central finding has two parts. First, where an edit should be applied transfers between them: the same early-to-mid-layer MLP at the last subject token is most effective for both. Second, this shared location does not guarantee a shared outcome. Single-token edits succeed in both, but as targets grow longer, editing degrades far more sharply in the MDMs than in the ARMs. The failure stems from how the edited fact is generated: producing a multi-token target passes through intermediate states in which the target is partially unmasked, for which the edit was never optimized. Guided by this diagnosis, we introduce a simple correction that optimizes the edit including such states, substantially restoring multi-token performance. Our code is available at https://github.com/holi-lab/MDM-KE.

Flooding is the most pervasive natural disaster worldwide. Timely and accurate flood inundation mapping are essential for informing disaster risk management. Optical satellite missions provide high-resolution, multispectral observations critical for flood detection and inundation mapping. However, their operational utility is severely constrained by cloud cover during extreme precipitation events. Conventional cloud-removal techniques based on temporal compositing or interpolation often fail to capture inundation dynamics. In this study, we introduce a cloud-removal framework for flood imagery based on Denoising Diffusion Probabilistic Models, leveraging the Masked Diffusion Transformer architecture. The proposed approach exploits self-attention mechanisms to capture wider spatial context and employs masked token modeling to explicitly learn the reconstruction of cloud-obscured regions. Trained on multispectral Sentinel-2B flood scenes with realistic cloud patterns, the model generates cloud-free image realizations that preserve both visual fidelity and hydrological consistency. Reconstruction performance is evaluated using standard image quality metrics alongside flood-specific hydrological measures, demonstrating improved continuity of water bodies and preservation of spectral signatures critical for water detection indices. The results indicate that diffusion-based generative modeling offers a robust and physically consistent alternative for cloud removal in optical flood monitoring, enabling more reliable, continuous observations to support disaster risk management and flood-related decision making.

Masked diffusion language models (MDLMs) re-predict every position at each denoising step, but standard samplers commit tokens once revealed, leaving this revision capability unused. Existing approaches either add heuristic or learned mechanisms to revise committed tokens, or remask them back to [MASK] before re-predicting; a principled sampler that directly revises visible tokens without auxiliary modules remains underexplored. We introduce D3IM, a parameter-free sampler derived as a corrector-style reverse update that permits direct visible-to-visible revision without additional modules or auxiliary passes. D3IM also reveals a model-side obstacle we term preservation bias: the model tends to reproduce its own wrong committed tokens rather than correct them. We address this with SCOPE (Self-Conditioned On Prediction Errors), a lightweight post-training procedure that simulates D3IM's sampling process. On LLaDA-8B at 64 denoising steps, SCOPE+D3IM improves over the original LLaDA-8B with standard unmasking by +13.0 on GSM8K (68.3%), +4.8 on MATH-500 (23.6%), +15.3 on HumanEval (29.3%), and +10.4 on MBPP (30.8%), with gains that increase as more denoising steps are used on math and HumanEval.

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

Masked diffusion models have seen great success in capturing data distributions over discrete sequences in domains such as text and proteins. These models generate data by iteratively unmasking tokens starting from a fully masked sequence, with the unmasking order typically chosen at random or using a heuristic based on denoiser probabilities. In this work, we propose a scheme for learning the unmasking order using an additional lightweight policy network on top of a diffusion model. Our proposed loss reweights terms in the masked diffusion loss according to policy probabilities, and results in a policy that prefers positions where the denoiser is more likely to be correct. We study this loss in two settings: (i) training solely the policy while using a frozen pre-trained denoiser, and (ii) training the policy and denoiser jointly with the weighted loss to allow for mutual adaptation. We demonstrate that our approach outperforms common heuristics on problems that are sensitive to token ordering, such as combinatorial tasks and proteins.

We present the first systematic study of masked diffusion language models (MDLMs) for graph-to-text generation. We analyze MDLM generation trajectories -- the order in which tokens are unmasked during iterative decoding -- and find that, unlike autoregressive LLMs which generate text linearly, MDLMs naturally prioritize entities first, followed by relational and function words, with structural tokens resolved last. We further identify a previously undocumented failure mode of supervised fine-tuning: SFT disrupts this strategy by prematurely anchoring structural sentence-ending tokens early in the decoding trajectory, effectively fixing the output length which can lead to omitted or hallucinated information. To address this, we propose lambda-scaled structural decoding, a training-free inference-time modification that downweights structural token confidence and recovers +9.4 BLEU-4. Finally, we introduce Graph-LLaDA, which integrates a Graph Transformer encoder into LLaDA's decoding process to explicitly incorporate relational graph structure. Cross-dataset evaluation on LAGRANGE reveals that previous baselines overfit to dataset-specific patterns, while LLM- and MDLM-based approaches generalize significantly better.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, \emph{CoFRe}. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8%, training time by 11.5%, and VRAM by 16.9%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6% and VRAM by 50.7%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

Anomaly detection aims to identify samples that deviate from the nominal data distribution and is central to many safety-critical applications. However, developing effective anomaly detection methods for categorical, mixed-type, and discrete sequence data remains challenging and relatively underexplored. Masked diffusion models provide a natural way to model such data by learning to recover masked values from the remaining visible context. In this paper, we propose Masked Diffusion for Anomaly Detection (MaskDiff-AD), a forward-only method based on masked diffusion models trained only on nominal data. Given a test sample, MaskDiff-AD constructs anomaly scores from the difficulty of reconstructing randomly masked coordinates, yielding a content-sensitive score that operates directly on discrete state spaces while avoiding reverse-time sampling. We also develop a non-parametric variant of MaskDiff-AD and provide theoretical guarantees by characterizing Type-I and Type-II errors under a fixed detection threshold. Experiments on fourteen categorical and mixed-type tabular datasets from ADBench and UADAD, as well as four text anomaly detection datasets from NLP-ADBench, show that MaskDiff-AD achieves competitive performance against classical, diffusion-based, and recent tabular/text anomaly detection baselines. Notably, MaskDiff-AD achieves the best overall average rank, outperforming all twelve tabular baseline methods.

Temporal action localization (TAL) requires recognizing the target event and localizing its start and end times precisely in untrimmed videos. Recent vision-language formulations improve semantic reasoning and support language-conditioned outputs, but their autoregressive decoders still generate tokens from left to right, preventing later semantic evidence from revising earlier timestamp predictions. We adapt masked diffusion vision-language models (MDVLMs) to TAL so that semantic tokens and boundary tokens remain editable throughout iterative denoising with bidirectional attention, allowing temporal boundaries and semantic content to be refined jointly. Direct adaptation, however, creates two TAL-specific mismatches: standard masked diffusion training corrupts all positions uniformly at random, but the time tokens are more reliable when enough semantic context is available; and token-level cross-entropy does not reflect temporal IoU. To address these mismatches, we introduce a Planned Training Objective that uses boundary-aware masking and step-weighted reconstruction to rehearse the late recovery of time tokens, together with a Step-Level IoU Reward that provides overlap-aware supervision during denoising. A standard sequence-level cross-entropy term provides the base reconstruction signal. Experiments on ActivityNet-RTL, ActivityNet-1.3, and THUMOS-14 show that MDVLM-TAL improves both temporal reasoning and boundary localization over autoregressive vision-language baselines, with especially strong gains under stricter temporal IoU criteria.

Masked diffusion language models (MDLMs) enable parallel decoding by predicting all masked positions at each denoising step, yet existing training-free samplers usually decide which positions to commit at token-level granularity. We revisit this granularity and observe that reliable predictions often emerge as contiguous high-confidence spans, suggesting that the unit of parallel commitment can be larger than a single token. We first group adjacent high-confidence candidates into confidence-induced clusters (CICs) as span-level update units. We then use self-attention maps from the same forward pass to estimate inter-cluster dependencies, enabling conflict-aware selection of mutually compatible CICs for parallel commitment. This yields CLAD (Cluster-Level Attention-Guided Decoding), a training-free cluster-level decoder for MDLMs. Experiments on LLaDA and Dream model families across four reasoning and code-generation benchmarks show that CLAD achieves 1.77x--8.47x speedups over Vanilla decoding while maintaining broadly comparable task accuracy in most settings.

Masked diffusion language models (MDMs) uniquely support any-order generation, with confidence-based decoding currently serving as the de facto standard inference policy. To optimize for this, recent training schemes attempt to align training mask patterns directly with those observed during generation. However, we argue that confidence-based decoding is inherently misaligned with the logical-flow trajectories required for complex reasoning, and that confidence-aligned training actively entrenches this misalignment. We make this concrete using multi-digit addition, where the decoding strategy prematurely predicts locally easy digits before resolving their long-range dependencies, producing high-confidence errors on challenging inputs. While traditional random masking keeps the failure rate low on this challenging tail, confidence-aligned training amplifies the error rate by an order of magnitude. Across five distinct reasoning tasks, this same pattern emerges with task-dependent severity: confidence-based decoding induces failures on highly complex inputs, and confidence-aligned training exacerbates them. In contrast, random masking -- despite its perceived inefficiency -- robustly preserves the reasoning-trajectory conditionals essential for solving the challenging tail.

Masked language modeling has become a standard pretraining objective for training encoder-based language models. In this approach, certain tokens in the input are masked, and the model learns to predict them using the surrounding context. This process enables the model to capture both syntactic and semantic properties of language. Conventionally, the tokens selected for masking are chosen at random, which may not always yield the most effective learning signals. In this work, we examine a token masking strategy based on entropy distribution. We use the model's entropy over token predictions to identify which tokens should be masked. This method aims to target tokens that are more informative and uncertain to improve the training efficacy. We also propose a novel self-masking approach that enhances training efficiency without relying on an external reference model. Experimental results demonstrate that our method achieves an average performance improvement of 5% in GLUE scores compared to the baseline. Further, we experiment with combining knowledge distillation with entropy masking, resulting in the best overall results.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models for language modeling, yet the effective design of transformer architectures for MDMs remains underexplored. In this paper, we show that selectively looping the early-middle transformer layers significantly improves both training efficiency and model performance in MDMs. We call this approach LoopMDM(Looped Masked Diffusion Model), which brings two key benefits: looping layers at training-time yields a depth-scaling effect without adding parameters, while varying the number of loops at inference-time enables flexible compute scaling. Despite the simplicity, the results are striking: across multiple pre-training corpora, LoopMDM matches the performance of same-size MDMs with up to 3.3 fewer training FLOPs, while its final performance outperforms them on various reasoning benchmarks, including up to 8.5 points on GSM8K. It even surpasses deeper non-looped MDMs trained with comparable per-step compute, indicating that selective looping is more effective than naive depth scaling. Furthermore, LoopMDM can scale inference-time compute by increasing the number of loops. Adaptively adjusting the number of loops throughout the sampling process further yields additional gains in compute efficiency while maintaining performance. Lastly, with attention analysis, we provide evidence that looping is effective in MDMs by promoting interactions among masked positions. Our code and weights will be publicly released.

Joint Embedding Predictive Architectures (JEPAs) have reshaped self-supervised representation learning in vision. The recent LLM-JEPA ported JEPA to autoregressive language models but inherited two steep costs from the causal-attention substrate: it demands explicit multi-view data (e.g., text-code pairs), and it requires two gradient-carrying forward passes per step. We introduce DLLM-JEPA, which pairs JEPA with masked-diffusion language models to eliminate both costs at once. The bidirectional attention of diffusion models yields two semantically distinct views of the same input via different masking rates -- no explicit pairs needed -- and supports a single gradient-carrying forward pass, cutting training FLOPs by 33% relative to LLM-JEPA. DLLM-JEPA improves over diffusion-only fine-tuning in every (task, architecture) combination we evaluate: up to +18.7 pp on LLaDA-8B GSM8K and +11.4 pp on Dream-7B GSM8K, with consistent positive gains on Spider, NL-RX-SYNTH, and Django. Beyond accuracy, DLLM-JEPA exhibits a dual-win property: on LLaDA-8B with the Wide-t configuration, it simultaneously raises GSM8K accuracy (67.1 vs. 65.2, +1.8 pp), drives held-out Wikitext loss below the pre-trained base, and preserves MMLU accuracy at base level across three fine-tuning seeds -- whereas an L2-to-base parameter anchor matches baseline accuracy with no task gain. Layer-wise probing reveals the mechanism: a geometric-functional drift dissociation in which the fine-tuned backbone moves further from the pre-trained weights than the baseline yet forgets less on held-out Wikitext, with the amplification concentrated in middle transformer layers. The pattern appears on Dream-7B as well, indicating the phenomenon is not specific to a single backbone.

When Masked Diffusion Models (MDMs) generate sequences through iterative refinement, the rich internal computation over masked positions is discarded, forcing every subsequent refinement step to recompute the valuable internal information stored as model representations. To avoid a hard reset between denoising rounds, we propose Learned Relay Representations (Relay), a method that allows MDMs to be forward-thinking when denoising by explicitly learning how to propagate latent information for the benefit of future denoising steps. Relay introduces a differentiable per-token channel that passes information between forward passes and is trained via truncated backpropagation through time (BPTT). We show that this framework can be scaled to state-of-the-art Diffusion Language Models (DLMs), and is seamlessly compatible with techniques like block diffusion and KV caching. We first provide a thorough justification of the design choices in Relay on a challenging Sudoku-based planning task. We then scale Relay to Fast-dLLM v2, a state-of-the-art DLM, outperforming standard supervised finetuning on coding tasks while reducing inference latency by up to 32%. Our empirical results demonstrate that state-of-the-art DLMs can be explicitly trained to relay latent information forward across decoding steps, advancing the performance-latency Pareto frontier. We provide code for all our experiments.

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

Masked diffusion language models (MDLMs) are emerging as a compelling new paradigm for text generation, but their training-time security remains largely unexplored. Existing backdoor attacks on Gaussian diffusion models or autoregressive language models do not directly apply to MDLMs because MDLMs rely on discrete state corruption and iterative denoising rather than continuous noising or left-to-right prediction. In this work, we present the first systematic study of training-time backdoor attacks on MDLMs. We propose SHADOWMASK, a backdoor attack that modifies the MDLM forward corruption process by replacing the standard all-mask terminal distribution with a trigger-mask mixture prior. This creates a dedicated denoising pathway from trigger-corrupted states to attacker-specified targets while preserving clean denoising behavior. We further provide a principled mathematical formulation by defining the backdoored forward process, deriving the reverse-time posterior, and obtaining the continuous-time training objective. Evaluations on DiT-based MDLM and LLaDA-8B-Instruct across WikiText-103, OpenWebText, and Alpaca show that SHADOWMASK achieves near-100% attack success, substantially outperforms standard data poisoning, largely preserves clean utility, remains effective under full-model and parameter-efficient fine-tuning, and is robust against representative defenses.

Recent masked diffusion language models (MDLMs), such as LLaDA and Dream, have achieved performance comparable to autoregressive large language models. Unlike autoregressive models, which generate text sequentially, MDLMs generate text by iteratively denoising masked positions in parallel. During fine-tuning, MDLMs learn to recover responses from masked response states conditioned on a prompt, thereby shifting their predictions from a prompt-masked unconditional distribution toward a prompt-conditional distribution. Despite this distinct generative and fine-tuning mechanism, machine unlearning for MDLMs remains largely unexplored. In this paper, we propose Masked Diffusion Unlearning (MDU), the first unlearning framework for MDLMs, by revisiting the process of learning specific knowledge in terms of diffusion. Specifically, MDU minimizes a forward KL divergence from the prompt-conditional prediction to a prompt-masked unconditional anchor at every masked response position, with a temperature scaling parameter to control the privacy-utility trade-off. Our empirical results on standard benchmarks and MDLM backbones show that MDU achieves high unlearning performance compared to existing LLM unlearning methods. Code is available at https://github.com/leegeoru/MDU.

Radiology report generation (RRG) aims to automatically produce clinically accurate textual reports from medical images. Existing methods predominantly rely on autoregressive (AR) language models, whose causal dependency structure restricts generation to a unidirectional left-to-right process. This paradigm can induce sequence bias, where models tend to follow stereotypical token orders and high-frequency report templates rather than fully grounding generation in image-specific evidence. In this paper, we propose AnchorDiff, the first masked-diffusion framework for RRG that integrates knowledge-graph-derived clinical anchors into diffusion language modeling. By leveraging bidirectional context and iterative refinement, AnchorDiff mitigates the limitations of fixed-order autoregressive decoding. Specifically, we introduce a topology-aware training strategy that uses RadGraph-derived entity hierarchies to assign clinically important tokens differentiated masking protection and loss weights. We further design an inference-time rewriting strategy that detects unstable committed tokens through perturbation-based testing and selectively revises them during denoising. Extensive experiments on the MIMIC-CXR and MIMIC-RG4 benchmarks demonstrate that AnchorDiff achieves state-of-the-art (SOTA) performance, showing the effectiveness of clinically anchored masked diffusion for radiology report generation.

Masked language modeling (MLM) is the standard objective for training protein language models, typically implemented by randomly masking individual residues at a fixed rate (e.g., 15%). This practice implicitly assumes that all sequence positions contribute equally to representation learning. In downstream fitness prediction tasks, however, protein sequences are governed by three-dimensional structural dependencies and long-range residue contacts that induce strong nonlocal couplings between residues. We introduce Bucket Masking, a structure-aware masking strategy that selects groups of residues based on their proximity in three-dimensional space, preferentially masking structurally coupled regions during training. By conditioning the masking distribution on residue contacts, Bucket Masking shifts the learning objective toward modeling long-range interactions that are critical for protein function. Across four downstream protein fitness prediction tasks, Bucket Masking enables up to a 14% improvement over standard random masking, excelling at predicting higher-order mutational interactions. Through controlled ablations, we show that these improvements arise from mask placement rather than span size, establishing masking as a positional inductive bias.

Masked Diffusion Language Models MDLMs replace autoregressive generation with iterative demasking and their privacy properties are largely unstudied. We study membership inference attacks MIA on fine tuned MDLMs and show they are significantly more vulnerable than current grey box baselines suggest. We extract a 46 dimensional feature vector from the models reconstruction loss at four masking ratios and train XGBoost and MLP classifiers on top. On the MIMIR benchmark across six text domains XGBoost achieves mean AUC 0.878 peaking at 0.930 on Pile CC and beats the SAMA grey box baseline by 0.062 AUC on average. A leave one signal out ablation shows that the ELBO trajectory alone drives most of this with a mean drop of 0.130 when removed while attention features add almost nothing below 0.003. We also design a shadow model transfer attack where K equals 3 surrogate MDLMs trained on data from unrelated domains generate classifier labels with no access to the target domain. This achieves 0.858 mean AUC within 0.020 of the white box oracle and establishes shadow model transfer as a practical and near equally effective attack path.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models (ARMs) for language modeling. However, MDMs are known to learn substantially more slowly than ARMs, which may become problematic when scaling MDMs to larger models. Therefore, we ask the following question: how can we accelerate standard MDM training while maintaining its final performance? To this end, we first provide a detailed analysis of why MDM training is slow. We find that the main factor is the locality bias of language: the predictive information for a token is concentrated in nearby positions. We further investigate how this bias slows learning and suggest a simple yet effective remedy: bell-shaped time sampling as a training strategy. Notably, MDMs trained with our training recipe reach the same validation negative log-likelihood (NLL) up to $\sim4\times$ faster than standard training on One Billion Word Benchmark (LM1B). We also show faster improvements in generative perplexity, zero-shot perplexity, and downstream task performance on various benchmarks.

Masked Diffusion Models (MDMs) have emerged as a promising alternative to autoregressive models in language modeling, offering the advantages of parallel decoding and bidirectional context processing within a simple yet effective framework. Specifically, their explicit distinction between masked tokens and data underlies their simple framework and effective conditional generation. However, MDMs typically require many sampling iterations due to factorization errors stemming from simultaneous token updates. We observe that a theoretical lower bound of the factorization error exists, which standard MDMs cannot reduce due to their use of a deterministic single-state mask. In this paper, we propose the Infinite Mask Diffusion Model (IMDM), which introduces a stochastic infinite-state mask to mitigate the theoretical bound while directly inheriting the benefits of MDMs, including the compatibility with pre-trained weights. We empirically demonstrate that MDM fails to perform few-step generation even in a simple synthetic task due to the factorization error bound, whereas IMDM can find an efficient solution for the same task. Finally, when equipped with appropriate distillation methods, IMDM surpasses existing few-step distillation methods at small step counts on LM1B and OpenWebText. Code is available at https://Ugness.github.io/official_imdm.

Masked diffusion language models enable parallel token generation and offer improved decoding efficiency over autoregressive models. However, their performance degrades significantly when generating multiple tokens simultaneously, due to a mismatch between token-level training objectives and joint sequence consistency. In this paper, we propose ME-DLM, an edit-based refinement framework that augments diffusion generation with lightweight post-editing steps. After producing an initial complete response, the model refines it through minimal edit operations, including replacement, deletion, and insertion, conditioned on the full sequence. Training supervision is derived from edit distance, providing a deterministic signal under a fixed canonicalization scheme for learning minimal corrections. This approach encourages sequence-level consistency through globally conditioned edits while preserving the efficiency benefits of parallel diffusion decoding. Extensive experiments demonstrate that ME-DLM improves the quality and robustness of multi-token parallel generation. In particular, when built upon LLaDA, our method achieves consistent gains of 11.6 points on HumanEval and 33.6 points on GSM8K while using one-eighth of the total diffusion steps. Code is available at https://github.com/renhouxing/ME-DLM.