SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions

Generative planners based on flow matching (FM) produce high-quality paths in a single or a few ODE steps, but their sampling dynamics offer no formal safety guarantees and can yield incomplete paths near constraints. We present SafeFlow-Matcher, a planning framework that couples FM with control barrier functions (CBFs) to achieve both real-time efficiency and certified safety. SafeFlowMatcher uses a two-phase prediction-correction (PC) integrator: (i) a prediction phase integrates the learned FM once (or a few steps) to obtain a candidate path without intervention; (ii) a correction phase refines this path with a vanishing time-scaled vector field and a CBF-based quadratic program that minimally perturbs the vector field. We prove a barrier certificate for the resulting flow system, establishing forward invariance of a robust safe set and finite-time convergence to the safe set. In addition, by enforcing safety only on the executed path-rather than all intermediate latent paths-SafeFlowMatcher avoids distributional drift and mitigates local trap problems. Moreover, SafeFlowMatcher attains faster, smoother, and safer paths than diffusion-and FM-based baselines on maze navigation, locomotion, and robot manipulation tasks. Extensive ablations corroborate the contributions of the PC integrator and the barrier certificate. Code is available at the project page.