CARM: Cancellation-Aware Response Masking for LLM Reinforcement Learning

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 for large language models (LLMs) typically relies on trust-region masks to stabilize off-policy updates. The dominant PPO-style approach uses the sampled-token importance ratio for two criteria: a proximity criterion, which asks whether the policy has moved too far from the behavior policy, and a direction criterion, which asks whether the update pushes it farther away. Recent work DPPO improves the proximity criterion by replacing PPO's ratio-based test with a probability divergence between the behavior and training policies. However, its direction criterion is still inherited from PPO. A token can be masked only when the sampled-token importance ratio moves away from one. We observe that this ratio-based direction criterion is a single-sample proxy that can disagree in sign with the change of the divergence that defines the proximity criterion. We therefore propose the predictive divergence mask, which asks whether the next policy-gradient step will increase or decrease the same divergence used by the trust region. For the discrete softmax policies used in LLM RL, we derive this prediction in closed form. Because production rollout engines expose only a truncated (top-K) view of the vocabulary, we develop two lightweight top-$K$ estimators for this prediction. Detailed analysis shows the divergence-based direction is better aligned with the realized change of the divergence than the sampled ratio, and the resulting masks improve RL training across model scales and precision settings.

Diffusion Large Language Models (dLLMs) have emerged as an efficient alternative to autoregressive models, yet aligning them via Reinforcement Learning (RL) requires likelihood surrogates estimated from masked reconstruction subproblems under a small Monte Carlo budget per rollout. Existing methods construct these subproblems by uniform random masking, leaving open the question of which subproblems to prioritize. We identify a systematic upstream/downstream structure in dLLM rollouts. Some tokens, when revealed, trigger large confidence changes in nearby undecoded positions; we call them upstream. Others induce only small local changes and are therefore downstream. We find masking downstream tokens yields substantially better-posed subproblems than masking upstream tokens, a phenomenon we term subproblem difficulty asymmetry. Based on the observation, we propose Informed Masking (IM), which derives a per-token priority score from the denoising trajectory at zero extra inference cost and biases mask sampling toward downstream tokens. IM is plug-and-play: when plugged into three state-of-the-art dLLM RL methods on LLaDA-8B-Instruct, it delivers up to 2.01%, 8.68%, and 5.77% relative average gains on math and planning benchmarks with improved training stability.