A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models
Authors: Zikun Zhang, Jiayuan Sheng, David D. Yao, Wenpin Tang
Abstract
We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC). We consider policy optimization problems and derive the corresponding policy gradient methods, leading to continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO). As a primary application, we develop a complete continuous-time RL framework for fine-tuning score-based discrete diffusion models. The proposed framework enables reward-driven optimization without requiring differentiability on the reward signals. In contrast to the existing GRPO-based approaches that only rely on terminal rewards, our formulation allows intermediate reward or advantage signals to be incorporated throughout the denoising trajectory. Importantly, when specialized to masked diffusion models (MDMs), our framework encompasses a rich class of policy parameterizations over the vocabulary simplex with analytically tractable probability ratios, providing a unified perspective on exploration and policy optimization in MDMs. For masked diffusion large language models (dLLMs), we further propose trajectory subsampling techniques to efficiently estimate computationally prohibitive trajectory likelihoods, reducing the computational cost of computing per-position probability ratios. We showcase the effectiveness of our methods on both low-dimensional entropy-regularized optimization problems and RL post-training of dLLMs on mathematical reasoning and coding tasks.
Diffusion large language models are a compelling alternative to autoregressive models, yet existing RL methods for diffusion treat all denoising steps as equally important and rely on biased, high-variance likelihood estimates. We identify two fundamental weaknesses: the absence of temporal credit assignment across the denoising trajectory, and the systematic bias of mean-field likelihood estimates used for policy optimization. To address these, we propose Denoising-Aware Credit Assignment for GRPO (DACA-GRPO), a lightweight, plug-and-play enhancement for any GRPO-style trainer. DACA-GRPO introduces two complementary mechanisms: Denoising Progress Scores, which extract per-token importance weights from intermediate predictions at no additional forward cost, and Stratified Masking Likelihood, which partitions token positions into strata so that each token is predicted with most of the sequence as context, reducing the mean-field bias. Applied on top of three GRPO base methods, DACA-GRPO achieves consistent improvements across seven benchmarks spanning mathematical reasoning, code generation, constraint satisfaction, and constrained generation, with gains of up to 5.6pp on math reasoning, 7.4pp on code generation, 36.3pp on constraint satisfaction, and 5.9pp on JSON schema adherence.
Reinforcement learning has proven effective for improving reasoning in large language models, but extending it to Masked Diffusion Language Models (MDLMs) remains challenging due to the intractability of the log-likelihood estimation. Existing approaches approximate this log-likelihood by modeling only the token predictions, ignoring the order in which positions are unmasked during generation. We observe that MDLM generation involves two decisions at each step: what tokens to place at each masked position and which positions to remask. We formalize this as a two-stage action MDP, showing that the policy gradient naturally decomposes into a token term and a masking term. Combining optimization of both terms leads to state-of-the-art outcomes on mathematical reasoning and coding benchmarks, with scores of 87.1% on GSM8K and 53.4% on MBPP.
Reinforcement learning (RL) holds immense promise for enhancing the reasoning capabilities of diffusion large language models (dLLMs). However, progress is fundamentally constrained by a dual misalignment between authentic generation trajectory and the gradient update process: (i) Process-reward misalignment. Sparse, terminal rewards are indiscriminately assigned to all intermediate steps of the generation process, failing to provide discriminative credit assignment. (ii) State-trajectory misalignment. Policy updates are often diverted toward artificial, out-of-trajectory states, squandering gradients on less informative samples. To address these limitations, we introduce Process Aligned Policy Optimization (PAPO), a novel framework that holistically aligns the RL update with the dLLM's generative trajectory via Step-Aware Process Rewards (SPR) that transform sparse terminal rewards into dense, step-wise credit, and Entropy-Guided Historical Re-enactment (EHR) that replays authentic trajectories at high-uncertainty steps. Extensive experiments on four benchmarks demonstrate that PAPO significantly outperforms baselines, achieving gains of up to 4.5% on GSM8K, 4.8% on MATH500, 42.2% on Countdown and 16.1% on Sudoku.