Flow Reasoning Models Achieve High Accuracy via Self-Refinement

Discrete flow models, while promising for text generation, often struggle with structured reasoning tasks, converging confidently to incorrect answers. This paper introduces Flow Reasoning Models (FRMs), a framework that scales reasoning through iterative self-refinement. The core insight is that flow models can act as their own verifiers: a correct answer is a stable fixed point under denoising dynamics. This enables a test-time scaling paradigm where multiple candidate solutions are proposed, and only dynamically stable ones are kept, leading to high solve rates on complex puzzles like Sudoku and Zebra. To further enhance efficiency, FRMs are trained with a self-conditioning channel for refinement and use direct preference optimization to avoid failed generations. This combined approach drastically improves the base model's efficiency, requiring significantly fewer passes for high accuracy and demonstrating strong generalization to out-of-distribution problems.