Masked diffusion language models (MDMs) have recently emerged as a promising alternative to standard autoregressive large language models (AR-LLMs), yet their optimization can be substantially less stable. We study blockwise MDMs and compare them with AR-LLMs on three controlled tasks that stress different aspects of structured generation: in-context linear regression, graph path-finding, and Sudoku solving. We find that standard random-masking MDMs fail to reliably learn linear regression, exhibit high variance training dynamics on graph path-finding, while outperforming AR-LLMs on Sudoku. To mitigate these instabilities, we propose two locality aware blockwise models, namely Jigsaw and Scatter, that inject left-to-right inductive bias by enforcing autoregressive locality within blocks while preserving iterative refinement at the block level. Empirically, Jigsaw matches AR-LLM stability on linear regression and remains strong on Sudoku, while Scatter retains diffusion's planning advantage on path-finding. Our results indicate that standard random-masking MDMs, even with blockwise variants, may be a suboptimal instantiation of diffusion LMs for ordered generation, motivating models beyond random masking.
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 ∼4× 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.
Post-training pretrained autoregressive models (ARMs) into masked diffusion models (MDMs) provides an efficient route to diffusion language modeling, but it remains unclear whether the resulting models reuse inherited autoregressive computation or reorganize it for non-autoregressive generation. We compare two 7B ARM-MDM families across four controlled diagnostic tasks and find a task-dependent mechanism shift. On prefix-dominant tasks, MDMs largely preserve inherited high-attribution pathways or exhibit only modest changes in where computation occurs. On globally constrained tasks, the reorganization is substantially stronger, with task-relevant computation shifting toward earlier layers. This depth-wise pattern persists across prompt resampling, circuit budgets, and tested inference budgets, while targeted ablations support the functional importance of the identified structures under the tested intervention protocols. At the component level, diagnostic probes suggest that ARMs rely more strongly on sharply specialized components, whereas MDMs exhibit weaker single-component specialization and more diffuse output-space alignment. Together, these results suggest that diffusion post-training selectively preserves or reorganizes inherited computation according to task structure, rather than uniformly replacing autoregressive mechanisms.
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.