We propose FlowRL: matching the full reward distribution via flow balancing instead of maximizing rewards in large language model (LLM) reinforcement learning (RL). Recent advanced reasoning models adopt reward-maximizing methods (\eg, PPO and GRPO), which tend to over-optimize dominant reward signals while neglecting less frequent but valid reasoning paths, thus reducing diversity. In contrast, we transform scalar rewards into a normalized target distribution using a learnable partition function, and then minimize the reverse KL divergence between the policy and the target distribution. We implement this idea as a flow-balanced optimization method that promotes diverse exploration and generalizable reasoning trajectories. We conduct experiments on math and code reasoning tasks: FlowRL achieves a significant average improvement of 10.0% over GRPO and 5.1% over PPO on math benchmarks, and performs consistently better on code reasoning tasks. These results highlight reward distribution-matching as a key step toward efficient exploration and diverse reasoning in LLM reinforcement learning.
@article{arxiv.2509.15207,
title = {FlowRL: Matching Reward Distributions for LLM Reasoning},
author = {Xuekai Zhu and Daixuan Cheng and Dinghuai Zhang and Hengli Li and Kaiyan Zhang and Che Jiang and Youbang Sun and Ermo Hua and Yuxin Zuo and Xingtai Lv and Qizheng Zhang and Lin Chen and Fanghao Shao and Bo Xue and Yunchong Song and Zhenjie Yang and Ganqu Cui and Ning Ding and Jianfeng Gao and Xiaodong Liu and Bowen Zhou and Hongyuan Mei and Zhouhan Lin},
journal= {arXiv preprint arXiv:2509.15207},
year = {2025}
}