# Parallelism and Generation Order in Masked Diffusion Language Models: Limits Today, Potential Tomorrow

arXiv: https://arxiv.org/abs/2601.15593 · HTML: https://mlsanity.com/paper/2601.15593/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 50 of its 71 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 50)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Stanza: A Python Natural Language Processing Toolkit for Many Human Languages](https://mlsanity.com/paper/2003.07082/) (2020)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [MuSR: Testing the Limits of Chain-of-thought with Multistep Soft Reasoning](https://mlsanity.com/paper/2310.16049/) (2023)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)

## Built on by (most cited first, 11 of 11)

- [Swordsman: Entropy-Driven Adaptive Block Partition for Efficient Diffusion Language Models](https://mlsanity.com/paper/2602.04399/) (2026)
- [Locally Coherent Parallel Decoding in Diffusion Language Models](https://mlsanity.com/paper/2603.20216/) (2026)
- [Neither Parallel Nor Sequential: How DiffusionGemma Actually Commits Tokens](https://mlsanity.com/paper/2606.14620/) (2026)
- [Fast-dLLM++: Fr'echet Profile Decoding for Faster Diffusion LLM Inference](https://mlsanity.com/paper/2606.02955/) (2026)
- [PSD: Pushing the Pareto Frontier of Diffusion LLMs via Parallel Speculative Decoding](https://mlsanity.com/paper/2605.15609/) (2026)
- [Visual-Redundancy-Controlled Parallel Decoding for Diffusion-Based Multimodal Large Language Models](https://mlsanity.com/paper/2605.25820/) (2026)
- [Conditional Total Correlation and the Serial Depth of Adaptive Parallel Sampling](https://mlsanity.com/paper/2608.25505/) (2026)
- [Decoding in Order-Agnostic Language Models: Chain-Rule Deviation and Uniform Spreading](https://mlsanity.com/paper/2606.00997/) (2026)
- [Plan Canvas: Fixed Reasoning Regions for Continuous Language Flows](https://mlsanity.com/paper/2610.05815/) (2026)
- [Intent-Triggered Anchoring for Multi-Token Format Units in Parallel Decoding of Diffusion Language Models](https://mlsanity.com/paper/2610.16516/) (2026)
- [TRACESTEER: Trace Driven Activation Steering for Hallucination Mitigation in Diffusion Language Models](https://mlsanity.com/paper/2610.18173/) (2026)

## Abstract (arXiv)

Masked Diffusion Language Models (MDLMs) promise parallel token generation and arbitrary-order decoding, yet it remains unclear to what extent current models truly realize these capabilities. We characterize MDLM behavior along two dimensions -- parallelism strength and generation order -- using Average Finalization Parallelism (AFP) and Kendall's tau. We evaluate eight mainstream MDLMs (up to 100B parameters) on 58 benchmarks spanning knowledge, reasoning, and programming. The results show that MDLMs still lag behind comparably sized autoregressive models, mainly because parallel probabilistic modeling weakens inter-token dependencies. Meanwhile, MDLMs exhibit adaptive decoding behavior: their parallelism and generation order vary significantly with the task domain, the stage of reasoning, and whether the output is correct. On tasks that require "backward information" (e.g., Sudoku), MDLMs adopt a solution order that tends to fill easier Sudoku blanks first, highlighting their advantages. Finally, we provide theoretical motivation and design insights supporting a Generate-then-Edit paradigm, which mitigates dependency loss while retaining the efficiency of parallel decoding.