Discrete Tilt Matching

• URL: http://arxiv.org/abs/2604.18739v1
• Date: Mon, 20 Apr 2026 18:43:37 GMT
• Title: Discrete Tilt Matching
• Abstract summary: Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation.<n>We derive Discrete Tilt Matching (DTM), a likelihood-free method that recasts dLLM fine-tuning as state-level matching of local unmasking posteriors.<n>DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.
• Score: 10.240234517598378
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. While reinforcement learning (RL) methods have recently been adapted to dLLM fine-tuning, their objectives typically depend on sequence-level marginal likelihoods, which are intractable for masked diffusion models. To address this, we derive Discrete Tilt Matching (DTM), a likelihood-free method that recasts dLLM fine-tuning as state-level matching of local unmasking posteriors under reward tilting. DTM takes the form of a weighted cross-entropy objective with explicit minimizer, and admits control variates that improve training stability. On a synthetic maze-planning task, we analyze how DTM's annealing schedule and control variates affect training stability and prevent mode collapse. At scale, fine-tuning LLaDA-8B-Instruct with DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.

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