Consistency Flow Matching (Consistency-FM) is a novel framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Unlike recent approaches that straighten flow trajectories through iterative rectification or optimal transport solutions, Consistency-FM explicitly enforces self-consistency in the velocity field. This method defines straight flows starting from different times to the same endpoint, constraining their velocity values. To enhance expressiveness, a multi-segment training approach is proposed, allowing for better transportation between complex distributions. Experiments on the CIFAR-10 dataset demonstrate that Consistency-FM converges 4.4 times faster than consistency models and 1.7 times faster than rectified flow models while achieving superior generation quality. The code for Consistency-FM is available at <https://github.com/YangLing0818/consistency_flow_matching>.Consistency Flow Matching (Consistency-FM) is a novel framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Unlike recent approaches that straighten flow trajectories through iterative rectification or optimal transport solutions, Consistency-FM explicitly enforces self-consistency in the velocity field. This method defines straight flows starting from different times to the same endpoint, constraining their velocity values. To enhance expressiveness, a multi-segment training approach is proposed, allowing for better transportation between complex distributions. Experiments on the CIFAR-10 dataset demonstrate that Consistency-FM converges 4.4 times faster than consistency models and 1.7 times faster than rectified flow models while achieving superior generation quality. The code for Consistency-FM is available at <https://github.com/YangLing0818/consistency_flow_matching>.