LFPO: Likelihood-Free Policy Optimization for Masked Diffusion Models
This work addresses a fundamental bottleneck in aligning diffusion models for domains requiring correctness, such as code generation and mathematical reasoning, representing a novel method rather than an incremental improvement.
The paper tackles the problem of applying reinforcement learning with verifiable rewards to diffusion large language models, which is hindered by intractable likelihood computation, and proposes LFPO, a likelihood-free policy optimization framework that outperforms state-of-the-art baselines on code and reasoning benchmarks while accelerating inference by approximately 20%.
Reinforcement Learning with Verifiable Rewards (RLVR) has achieved remarkable success in improving autoregressive models, especially in domains requiring correctness like mathematical reasoning and code generation. However, directly applying such paradigms to Diffusion Large Language Models (dLLMs) is fundamentally hindered by the intractability of exact likelihood computation, which forces existing methods to rely on high-variance approximations. To bridge this gap, we propose Likelihood-Free Policy Optimization (LFPO), a native framework that maps the concept of vector field flow matching to the discrete token space. Specifically, LFPO formulates alignment as geometric velocity rectification, which directly optimizes denoising logits via contrastive updates. This design effectively bypasses the errors inherent in likelihood approximation, yielding the precise gradient estimation. Furthermore, LFPO enforce consistency by predicting final solutions from intermediate steps, effectively straightening the probability flow to enable high-quality generation with significantly fewer iterations. Extensive experiments demonstrate that LFPO not only outperforms state-of-the-art baselines on code and reasoning benchmarks but also accelerates inference by approximately 20% through reduced diffusion steps.