Discrete Tilt Matching

Yuyuan Chen, Shiyi Wang, Peter Potaptchik, Jaeyeon Kim, Michael Samuel Albergo
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:17141-17164, 2026.

Abstract

Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. While reinforcement learning (RL) algorithms have been adapted to be compatible with dLLMs for fine-tuning them, their reliance on the computation of the marginal likelihood to evaluate policy objectives is intractable. To overcome this, we exploit a dynamical relation between the unmasking posterior of the base model and that which targets the reward-tilted distribution to derive Discrete Tilt Matching (DTM), an algorithm that avoids intractable likelihood evaluation entirely. DTM can be phrased as a cross-entropy loss that only requires forward evaluation of rewards and whose variance can be adaptively controlled, improving training stability. We motivate DTM on maze planning tasks, and show that fine-tuning LLaDA-8B-Instruct with DTM achieves higher accuracy at lower compute costs than prior RL-based fine-tuning methods across the Sudoku, Countdown, and MATH500 benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-chen26el, title = {Discrete Tilt Matching}, author = {Chen, Yuyuan and Wang, Shiyi and Potaptchik, Peter and Kim, Jaeyeon and Albergo, Michael Samuel}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {17141--17164}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/chen26el/chen26el.pdf}, url = {https://proceedings.mlr.press/v306/chen26el.html}, abstract = {Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. While reinforcement learning (RL) algorithms have been adapted to be compatible with dLLMs for fine-tuning them, their reliance on the computation of the marginal likelihood to evaluate policy objectives is intractable. To overcome this, we exploit a dynamical relation between the unmasking posterior of the base model and that which targets the reward-tilted distribution to derive Discrete Tilt Matching (DTM), an algorithm that avoids intractable likelihood evaluation entirely. DTM can be phrased as a cross-entropy loss that only requires forward evaluation of rewards and whose variance can be adaptively controlled, improving training stability. We motivate DTM on maze planning tasks, and show that fine-tuning LLaDA-8B-Instruct with DTM achieves higher accuracy at lower compute costs than prior RL-based fine-tuning methods across the Sudoku, Countdown, and MATH500 benchmarks.} }
Endnote
%0 Conference Paper %T Discrete Tilt Matching %A Yuyuan Chen %A Shiyi Wang %A Peter Potaptchik %A Jaeyeon Kim %A Michael Samuel Albergo %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-chen26el %I PMLR %P 17141--17164 %U https://proceedings.mlr.press/v306/chen26el.html %V 306 %X Masked diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. While reinforcement learning (RL) algorithms have been adapted to be compatible with dLLMs for fine-tuning them, their reliance on the computation of the marginal likelihood to evaluate policy objectives is intractable. To overcome this, we exploit a dynamical relation between the unmasking posterior of the base model and that which targets the reward-tilted distribution to derive Discrete Tilt Matching (DTM), an algorithm that avoids intractable likelihood evaluation entirely. DTM can be phrased as a cross-entropy loss that only requires forward evaluation of rewards and whose variance can be adaptively controlled, improving training stability. We motivate DTM on maze planning tasks, and show that fine-tuning LLaDA-8B-Instruct with DTM achieves higher accuracy at lower compute costs than prior RL-based fine-tuning methods across the Sudoku, Countdown, and MATH500 benchmarks.
APA
Chen, Y., Wang, S., Potaptchik, P., Kim, J. & Albergo, M.S.. (2026). Discrete Tilt Matching. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:17141-17164 Available from https://proceedings.mlr.press/v306/chen26el.html.

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