SPG: Sandwiched Policy Gradient for Masked Diffusion Language Models

arXiv:2510.09541v3 Announce Type: replace Abstract: Diffusion large language models (dLLMs) are emerging as an efficient alternative to autoregressive models due to their ability to decode multiple tokens in parallel. However, aligning dLLMs with human preferences or task-specific rewards via reinforcement learning (RL) is challenging because their intractable log-likelihood precludes the direct application of standard policy gradient methods. While prior work uses surrogates like the evidence lower bound (ELBO), these one-sided approximations can introduce significant policy gradient bias. To address this, we propose the Sandwiched Policy Gradient (SPG) that leverages both an upper and a lower bound of the true log-likelihood. Experiments show that SPG significantly outperforms baselines based on ELBO or one-step estimation. Specifically, SPG improves the accuracy over state-of-the-art RL methods for dLLMs by 3.6% in GSM8K, 2.6% in MATH500, 18.4% in Countdown and 27.0% in Sudoku.

Related

• dTRPO: Trajectory Reduction in Policy Optimization of Diffusion Large Language Models
• SSPO: Subsentence-level Policy Optimization
• RL-PLUS: Countering Capability Boundary Collapse of LLMs in Reinforcement Learning with Hybrid-policy Optimization
• EEPO: Exploration-Enhanced Policy Optimization via Sample-Then-Forget
• AAPO: Enhancing the Reasoning Capabilities of LLMs with Advantage Margin

Source: arXiv cs.CL | 2026-04-16