# Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization

arXiv: https://arxiv.org/abs/2510.08233 · HTML: https://mlsanity.com/paper/2510.08233/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 90 of its 103 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)

## Builds on (most cited first, 30 of 90)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)

## Built on by (most cited first, 20 of 20)

- [Learning Unmasking Policies for Diffusion Language Models](https://mlsanity.com/paper/2512.09106/) (2025)
- [dUltra: Ultra-Fast Diffusion Language Models via Reinforcement Learning](https://mlsanity.com/paper/2512.21446/) (2025)
- [LaViDa-R1: Advancing Reasoning for Unified Multimodal Diffusion Language Models](https://mlsanity.com/paper/2602.14147/) (2026)
- [GDSD: Reinforcement Learning as Guided Denoiser Self-Distillation for Diffusion Language Models](https://mlsanity.com/paper/2605.29398/) (2026)
- [FLARE: Diffusion for Hybrid Language Model](https://mlsanity.com/paper/2606.01774/) (2026)
- [Diffusion Reinforcement Learning via Centered Reward Distillation](https://mlsanity.com/paper/2603.14128/) (2026)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [Discrete Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2602.08243/) (2026)
- [Back on Track: Aligning Rewards and States for Reasoning in Diffusion Large Language Models](https://mlsanity.com/paper/2606.08501/) (2026)
- [DPRM: A Plug-in Doob h transform-induced Token-Ordering Module for Discrete Diffusion Models](https://mlsanity.com/paper/2604.24357/) (2026)
- [Beyond Mode-Seeking RL: Trajectory-Balance Post-Training for Diffusion Language Models](https://mlsanity.com/paper/2605.13935/) (2026)
- [A2D2: Fine-Tuning Any-Length Discrete Diffusion for Adaptive Decoding](https://mlsanity.com/paper/2606.13565/) (2026)
- [Scheduling Thoughts: Learning the Order of Thought in Diffusion Language Models](https://mlsanity.com/paper/2606.23567/) (2026)
- [Graph Forward Distribution Matching for Molecular Inverse Design](https://mlsanity.com/paper/2609.32056/) (2026)
- [CT-OPD: Counterfactual Trace On-Policy Distillation for Diffusion Vision-Language Models](https://mlsanity.com/paper/2609.32781/) (2026)
- [Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models](https://mlsanity.com/paper/2610.00661/) (2026)
- [IDRF: Inverse-Distilled Reward Fine-tuning of Masked Discrete Diffusion Models](https://mlsanity.com/paper/2610.03641/) (2026)
- [RL Post-Training Diffusion Language Models Along Their Own Generation Paths](https://mlsanity.com/paper/2610.17266/) (2026)
- [HaloBlock: Faster and Better Decoding for Diffusion Large Language Models](https://mlsanity.com/paper/2610.17948/) (2026)
- [ForkGRPO: Efficient Exploration and Fine-Grained Credit Assignment for Diffusion Language Models](https://mlsanity.com/paper/2610.19408/) (2026)

## Abstract (arXiv)

Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is crucial to enabling dLLMs to achieve performance comparable to that of AR-LLMs on important tasks, such as reasoning. However, RL algorithms well-suited to dLLMs' unique characteristics have yet to be developed. This paper proposes Distribution Matching Policy Optimization (DMPO), a principled and theoretically grounded RL fine-tuning method specifically designed to enhance the reasoning capabilities of dLLMs by matching the dLLM policy distribution to the optimal, reward-tilted one through cross-entropy optimization. We identify a key implementation challenge with small training batch sizes and propose several effective solutions based on a novel weight baseline subtraction technique. DMPO exhibits superior performance on multiple reasoning benchmarks without supervised fine-tuning, achieving up to a 39.63 percentage-point improvement in accuracy over prior non-DMPO RL baselines and 67.97 percentage points over the base model, underscoring the effectiveness of the distribution-matching framework. Our code is available at https://github.com/yuchen-zhu-zyc/DMPO.