Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

翻译：流匹配（FM）是通过常微分方程（ODE）定义概率路径以在噪声与数据样本之间进行变换的通用框架。近期方法试图通过迭代校正方法或最优传输解来拉直这些流轨迹，从而以更少的函数评估次数生成高质量样本。本文提出一致性流匹配（Consistency-FM），这是一种新颖的FM方法，其显式强制速度场满足自洽性。Consistency-FM直接定义从不同时间出发到达同一终点的直线流，并对它们的速度值施加约束。此外，我们为Consistency-FM提出一种多段训练方法以增强表达能力，在采样质量与速度之间实现更好的权衡。初步实验表明，我们的Consistency-FM显著提升了训练效率：其收敛速度比一致性模型快4.4倍，比校正流模型快1.7倍，同时实现了更好的生成质量。我们的代码公开于：https://github.com/YangLing0818/consistency_flow_matching