wd1: Weighted Policy Optimization for Reasoning in Diffusion Language Models

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 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, \textit{wd1} outperforms diffusion-based GRPO (\textit{d1}) while requiring lower computational cost, achieving up to a $+59\%$ improvement in accuracy. Furthermore, we extend \textit{wd1} to denoising-stepwise weighted policy optimization (\algname++), achieving state-of-the-art math performance of $44.2\%$ on MATH500 and $84.5\%$ on GSM8K with only 20 RL training steps.