Efficient Paths and Dense Rewards: Probabilistic Flow Reasoning for Large Language Models

TL;DR

This paper introduces CoT-Flow, a probabilistic flow framework for large language models that improves reasoning efficiency and accuracy by quantifying step-wise information gain and guiding inference.

Contribution

It presents a novel probabilistic flow approach to model reasoning steps, enabling flow-guided decoding and dense reward reinforcement learning for better reasoning performance.

Findings

Improves inference efficiency by reducing redundant exploration.

Achieves higher reasoning accuracy on benchmark tasks.

Provides a verifier-free dense reward for training.

Abstract

High-quality chain-of-thought has demonstrated strong potential for unlocking the reasoning capabilities of large language models. However, current paradigms typically treat the reasoning process as an indivisible sequence, lacking an intrinsic mechanism to quantify step-wise information gain. This granularity gap manifests in two limitations: inference inefficiency from redundant exploration without explicit guidance, and optimization difficulty due to sparse outcome supervision or costly external verifiers. In this work, we propose CoT-Flow, a framework that reconceptualizes discrete reasoning steps as a continuous probabilistic flow, quantifying the contribution of each step toward the ground-truth answer. Built on this formulation, CoT-Flow enables two complementary methodologies: flow-guided decoding, which employs a greedy flow-based decoding strategy to extract information-efficient reasoning paths, and flow-based reinforcement learning, which constructs a verifier-free dense reward function. Experiments on challenging benchmarks demonstrate that CoT-Flow achieves a superior balance between inference efficiency and reasoning performance.