# RL Post-Training Diffusion Language Models Along Their Own Generation Paths

arXiv: https://arxiv.org/abs/2610.17266 · HTML: https://mlsanity.com/paper/2610.17266/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 33 of its 36 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

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

## Builds on (most cited first, 30 of 33)

- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [MMaDA: Multimodal Large Diffusion Language Models](https://mlsanity.com/paper/2505.15809/) (2025)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)
- [Bridging the Gap Between Value and Policy Based Reinforcement Learning](https://mlsanity.com/paper/1702.08892/) (2017)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2507.08838/) (2025)
- [Reinforcing the Diffusion Chain of Lateral Thought with Diffusion Language Models](https://mlsanity.com/paper/2505.10446/) (2025)
- [SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models](https://mlsanity.com/paper/2510.09541/) (2025)
- [FlowRL: Matching Reward Distributions for LLM Reasoning](https://mlsanity.com/paper/2509.15207/) (2025)
- [Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction](https://mlsanity.com/paper/2410.08134/) (2024)
- [Efficient Diversity-Preserving Diffusion Alignment via Gradient-Informed GFlowNets](https://mlsanity.com/paper/2412.07775/) (2024)
- [Trust-PCL: An Off-Policy Trust Region Method for Continuous Control](https://mlsanity.com/paper/1707.01891/) (2017)
- [Diffusion of Thoughts: Chain-of-Thought Reasoning in Diffusion Language Models](https://mlsanity.com/paper/2402.07754/) (2024)
- [Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization](https://mlsanity.com/paper/2510.08233/) (2025)
- [Simple Policy Gradients for Reasoning with Diffusion Language Models](https://mlsanity.com/paper/2510.04019/) (2025)
- [On the Reasoning Abilities of Masked Diffusion Language Models](https://mlsanity.com/paper/2510.13117/) (2025)
- [DiffuMamba: High-Throughput Diffusion LMs with Mamba Backbone](https://mlsanity.com/paper/2511.15927/) (2025)
- [GDSD: Reinforcement Learning as Guided Denoiser Self-Distillation for Diffusion Language Models](https://mlsanity.com/paper/2605.29398/) (2026)
- [Relative Trajectory Balance is equivalent to Trust-PCL](https://mlsanity.com/paper/2509.01632/) (2025)
- [Beyond Mode-Seeking RL: Trajectory-Balance Post-Training for Diffusion Language Models](https://mlsanity.com/paper/2605.13935/) (2026)
- [Mask-Aware Policy Gradients for Diffusion Language Models](https://mlsanity.com/paper/2607.15200/) (2026)
- [Discrete Tilt Matching](https://mlsanity.com/paper/2604.18739/) (2026)

## Abstract (arXiv)

Diffusion language models are a promising and more efficient alternative to autoregressive models. However, most RL post-training techniques are not easily adapted to these models. One issue is that diffusion language models generate answers through many intermediate states, deciding at each step which masked positions to reveal and which tokens to place in them. Many existing RL methods used in this setting approximate intractable sequence likelihoods or weight every denoising step by the same advantage, without explicitly distinguishing how these intermediate states of the denoising trajectory affect the expected reward. To address this issue of trajectory blindness, we introduce PACT (Potential-Anchored Consistency of Transitions). Motivated by a reward-tilted reference distribution, PACT jointly learns the policy and a scalar potential that scores each intermediate state, anchored by terminal reward. For each sampled denoising transition, a consistency loss matches the policy-to-reference log-probability ratio of revealed tokens to the change in this potential. This formulation requires neither sequence-likelihood estimation nor importance-ratio clipping. On four tasks, PACT improves LLaDA-8B-Instruct by +9.9 points on GSM8K, +12.0 on MATH500, +55.7 on Countdown, and +72.6 on Sudoku, and reaches the best average accuracy across the four tasks reported for this model, +3.7 points over the next best method. Further compared to AGRPO, it reaches that baseline's best accuracy in about half the training compute on GSM8K.