LFPO: Likelihood-Free Policy Optimization for Masked Diffusion Models

TL;DR

LFPO introduces a likelihood-free optimization framework for masked diffusion models, improving accuracy and efficiency by directly optimizing denoising logits and reducing diffusion steps, thus enhancing reasoning and code generation tasks.

Contribution

LFPO presents a novel likelihood-free policy optimization method that bypasses likelihood approximation errors in diffusion models, enabling more accurate and faster inference.

Findings

Outperforms state-of-the-art baselines on reasoning and code benchmarks.

Reduces inference diffusion steps by approximately 20%.

Achieves more precise gradient estimation through geometric velocity rectification.

Abstract

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.