Generative planners based on flow matching (FM) can generate high-quality paths in one or two ODE steps, but their sampling dynamics do not provide formal safety guarantees and can generate incomplete paths near constraints. In this paper, we present SafeFlowMatcher, a planning framework that combines FM and control barrier functions (CBFs) to achieve both real-time efficiency and certified safety. SafeFlowMatcher uses a two-step prediction-correction (PC) integrator. (i) The prediction step integrates the learned FM once (or several steps) to obtain candidate paths without intervention. (ii) The correction step refines these paths using a vanishing time-scale vector field and a CBF-based quadratic programming method that minimally perturbs the vector field. We prove a barrier certificate for the resulting flow system, establishing forward invariance of a robust safety set and finite-time convergence to the safety set. SafeFlowMatcher avoids distributional drift and mitigates the local trap problem by enforcing safety only on executed paths (rather than on all intermediate potential paths). In maze navigation and locomotion benchmarks, SafeFlowMatcher achieves faster, smoother, and safer paths than diffusion- and FM-based baselines. Extensive removal experiments support the contributions of the PC integrator and barrier certificate.
