CoT-Flow: Reshaping the Reasoning Paradigm of Large Language Models with Probabilistic Flow

This article introduces the ACL 2026 accepted paper CoT-Flow, whose core is to transform discrete reasoning steps into continuous probabilistic flows and quantify the contribution of each step to the correct answer via Probabilistic Flow Progress (PFP). This method achieves two major breakthroughs: inference acceleration without additional training, and reinforcement learning alignment based on dense rewards.

Current Chain-of-Thought (CoT) reasoning in LLMs has limitations: intermediate steps are discrete sequences, and there is a lack of mechanisms to quantify the information gain of each step. This leads to lengthy reasoning, high computational resource consumption, and sparse reward signals during training, making it difficult to achieve fine-grained alignment and optimization.

CoT-Flow proposes a unified framework that reconstructs discrete reasoning steps into continuous probabilistic flows. The core concept, Probabilistic Flow Progress (PFP), can quantify the contribution of each step to the correct answer. This framework has dual capabilities: using greedy flow decoding to select efficient paths during inference, and leveraging the accumulative nature of probabilistic flows to construct dense reward functions during training.

This module can extract efficient reasoning paths without additional training. By selecting tokens with high PFP scores, the system can find the shortest semantic path to the answer without external validators. Based on the SGLang framework, users can experience the acceleration effect by installing dependencies and running shell scripts.

This module integrates CoT-Flow into the reinforcement learning loop. It uses the accumulative nature of probabilistic flows to generate dense rewards, penalize redundant steps, and robustly align strategies. Based on the oat framework (referencing the VeriFree approach), dense rewards provide more fine-grained feedback than sparse rewards, making strategy optimization more stable and efficient.

In benchmark tests such as AIME 2024 and MATH-500, CoT-Flow achieves an excellent balance between inference efficiency and performance. The results show that while maintaining or even improving accuracy, it significantly reduces the number of reasoning steps, which is of great significance for LLM deployment in resource-constrained scenarios.

The codebase is divided into two sub-projects: cot-flow-greedy-decoding/ (inference optimization module) and cot-flow-rl/ (RL training module), with a modular design for easy reuse. The paper has been published on arXiv (2601.09260) and accepted by ACL 2026, and its open-source release provides new research directions and tools for the community.

CoT-Flow is a significant progress in chain-of-thought reasoning research, solving the problem of inference efficiency and providing new possibilities for RL alignment. It is a project worth paying attention to for researchers and engineers focusing on LLM reasoning optimization, efficient path search, and RL alignment.