# On the Trainability of Masked Diffusion Language Models via Blockwise Locality

arXiv: https://arxiv.org/abs/2604.24832 · HTML: https://mlsanity.com/paper/2604.24832/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 13 of 13)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [SDAR: A Synergistic Diffusion-AutoRegression Paradigm for Scalable Sequence Generation](https://mlsanity.com/paper/2510.06303/) (2025)
- [FlashDLM: Accelerating Diffusion Language Model Inference via Efficient KV Caching and Guided Diffusion](https://mlsanity.com/paper/2505.21467/) (2025)
- [Diffusion Language Models are Super Data Learners](https://mlsanity.com/paper/2511.03276/) (2025)
- [Plan for Speed: Dilated Scheduling for Masked Diffusion Language Models](https://mlsanity.com/paper/2506.19037/) (2025)
- [The Factorization Curse: Which Tokens You Predict Underlie the Reversal Curse and More](https://mlsanity.com/paper/2406.05183/) (2024)
- [Diffusion In Diffusion: Reclaiming Global Coherence in Semi-Autoregressive Diffusion](https://mlsanity.com/paper/2601.13599/) (2026)
- [Optimizing Decoding Paths in Masked Diffusion Models by Quantifying Uncertainty](https://mlsanity.com/paper/2512.21336/) (2025)

## Built on by (most cited first, 2 of 2)

- [Understanding Parallel Samplers in Masked Diffusion via Random Walks on Graphs](https://mlsanity.com/paper/2606.22976/) (2026)
- [Semantic DLM+: Improving Diffusion Language Models through Bias-variance Trade-off in Transition Kernel Design](https://mlsanity.com/paper/2606.15327/) (2026)

## Abstract (arXiv)

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.