Reinforcement Learning for Diffusion LLMs via Energy-Based Gibbs Alignment

Diffusion Large Language Models (dLLMs) have emerged as a promising non-autoregressive paradigm for text generation, offering parallel decoding and bidirectional context modeling. However, aligning dLLMs with reinforcement learning (RL) remains a significant challenge, as the marginal likelihood of sequences in masked diffusion is typically intractable, rendering standard policy gradient methods unstable or computationally prohibitive. In this work, we propose Diffusion-Gibbs Alignment (DGA), a novel variational framework that reformulates RL for dLLMs as a distribution matching problem. DGA bypasses the explicit computation of log-probabilities by leveraging a learned energy function to model the relative quality of samples. The optimization is decoupled into two stable steps: (1) contrastive energy ranking to capture global reward structures, and (2) weighted diffusion alignment to update the policy via importance sampling. Empirically, DGA establishes a new state-of-the-art across logical reasoning (Sudoku, Countdown), mathematical reasoning (GSM8K, Math500), and code generation (HumanEval, MBPP) benchmarks. DGA offers a novel variational perspective for dLLM alignment, achieving better performance while simultaneously enhancing training speed and memory efficiency.