# wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models

arXiv: https://arxiv.org/abs/2507.08838 · HTML: https://mlsanity.com/paper/2507.08838/

## Key facts

- Cited by 71 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 48 of its 67 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Placed in

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

## Builds on (most cited first, 30 of 48)

- [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)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [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)
- [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)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning](https://mlsanity.com/paper/1910.00177/) (2019)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks](https://mlsanity.com/paper/1911.04933/) (2019)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data](https://mlsanity.com/paper/2406.03736/) (2024)
- [LLaDA 1.5: Variance-Reduced Preference Optimization for Large Language Diffusion Models](https://mlsanity.com/paper/2505.19223/) (2025)
- [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)
- [Scaling up Masked Diffusion Models on Text](https://mlsanity.com/paper/2410.18514/) (2024)
- [Remasking Discrete Diffusion Models with Inference-Time Scaling](https://mlsanity.com/paper/2503.00307/) (2025)
- [d1: Scaling Reasoning in Diffusion Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2504.12216/) (2025)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)

## Built on by (most cited first, 30 of 71)

- [A Survey on Diffusion Language Models](https://mlsanity.com/paper/2508.10875/) (2025)
- [LLaDA-MoE: A Sparse MoE Diffusion Language Model](https://mlsanity.com/paper/2509.24389/) (2025)
- [SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models](https://mlsanity.com/paper/2510.09541/) (2025)
- [Don't Settle Too Early: Self-Reflective Remasking for Diffusion Language Models](https://mlsanity.com/paper/2509.23653/) (2025)
- [Principled RL for Diffusion LLMs Emerges from a Sequence-Level Perspective](https://mlsanity.com/paper/2512.03759/) (2025)
- [Improving Reasoning for Diffusion Language Models via Group Diffusion Policy Optimization](https://mlsanity.com/paper/2510.08554/) (2025)
- [A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Models](https://mlsanity.com/paper/2508.08712/) (2025)
- [Learning Unmasking Policies for Diffusion Language Models](https://mlsanity.com/paper/2512.09106/) (2025)
- [d2: Improving Reasoning in Diffusion Language Models via Trajectory Likelihood Estimation](https://mlsanity.com/paper/2509.21474/) (2025)
- [From Next-Token to Next-Block: A Principled Adaptation Path for Diffusion LLMs](https://mlsanity.com/paper/2512.06776/) (2025)
- [Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization](https://mlsanity.com/paper/2510.08233/) (2025)
- [DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning](https://mlsanity.com/paper/2510.02212/) (2025)
- [DMax: Aggressive Parallel Decoding for dLLMs](https://mlsanity.com/paper/2604.08302/) (2026)
- [d-TreeRPO: Towards More Reliable Policy Optimization for Diffusion Language Models](https://mlsanity.com/paper/2512.09675/) (2025)
- [Inpainting-Guided Policy Optimization for Diffusion Large Language Models](https://mlsanity.com/paper/2509.10396/) (2025)
- [Consolidating Reinforcement Learning for Multimodal Discrete Diffusion Models](https://mlsanity.com/paper/2510.02880/) (2025)
- [Simple Policy Gradients for Reasoning with Diffusion Language Models](https://mlsanity.com/paper/2510.04019/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [Breaking the Factorization Barrier in Diffusion Language Models](https://mlsanity.com/paper/2603.00045/) (2026)
- [Advancing Reasoning in Diffusion Language Models with Denoising Process Rewards](https://mlsanity.com/paper/2510.01544/) (2025)
- [dUltra: Ultra-Fast Diffusion Language Models via Reinforcement Learning](https://mlsanity.com/paper/2512.21446/) (2025)
- [Stabilizing Reinforcement Learning for Diffusion Language Models](https://mlsanity.com/paper/2603.06743/) (2026)
- [Test-Time Scaling in Diffusion LLMs via Hidden Semi-Autoregressive Experts](https://mlsanity.com/paper/2510.05040/) (2025)
- [RFG: Test-Time Scaling for Diffusion Large Language Model Reasoning with Reward-Free Guidance](https://mlsanity.com/paper/2509.25604/) (2025)
- [LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning](https://mlsanity.com/paper/2602.01705/) (2026)
- [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)
- [Learning from the Self-future: On-policy Self-distillation for dLLMs](https://mlsanity.com/paper/2606.18195/) (2026)
- [DreamReasoner-8B: Block-Size Curriculum Learning for Diffusion Reasoning Models](https://mlsanity.com/paper/2606.19257/) (2026)
- [GIFT: Guided Importance-Aware Fine-Tuning for Diffusion Language Models](https://mlsanity.com/paper/2509.20863/) (2025)

## Abstract (arXiv)

Improving the reasoning capabilities of diffusion-based large language models (dLLMs) through reinforcement learning (RL) remains an open problem. The intractability of dLLMs likelihood function necessitates approximating the current, old, and reference policy likelihoods at each policy optimization step. This reliance introduces additional computational overhead, and can lead to large variance and estimation error in RL objective -- particularly in computing the policy ratio for importance sampling. To mitigate these issues, we introduce wd1, a novel ratio-free policy optimization approach that reformulates the RL objective as a weighted log-likelihood, requiring only a single approximation for the current parametrized policy likelihood. We formally show that our proposed method can be interpreted as energy-guided discrete diffusion training combined with negative sample unlearning, thereby confirming its theoretical soundness. In experiments on LLaDA-8B model, wd1 outperforms diffusion-based GRPO (d1) while requiring lower computational cost, achieving up to a +59% improvement in accuracy. Furthermore, we extend wd1 to denoising-stepwise weighted policy optimization (wd1++), achieving state-of-the-art math performance of 44.2% on MATH500 and 84.5% on GSM8K with only 20 RL training steps.