Variational Reasoning for Language Models
Authors: name: Xiangxin Zhou; name: Zichen Liu; name: Haonan Wang; name: Chao Du; name: Min Lin; name: Chongxuan Li; name: Liang Wang; name: Tianyu Pang
Published: 2025-09-26 17:58:10

Abstract: We introduce a variational reasoning framework for language models that
treats thinking traces as latent variables and optimizes them through
variational inference. Starting from the evidence lower bound (ELBO), we extend
it to a multi-trace objective for tighter bounds and propose a forward-KL
formulation that stabilizes the training of the variational posterior. We
further show that rejection sampling finetuning and binary-reward RL, including
GRPO, can be interpreted as local forward-KL objectives, where an implicit
weighting by model accuracy naturally arises from the derivation and reveals a
previously unnoticed bias toward easier questions. We empirically validate our
method on the Qwen 2.5 and Qwen 3 model families across a wide range of
reasoning tasks. Overall, our work provides a principled probabilistic
perspective that unifies variational inference with RL-style methods and yields
stable objectives for improving the reasoning ability of language models. Our
code is available at https://github.com/sail-sg/variational-reasoning.