Title: SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions
Primary area: applications to robotics, autonomy, planning
Keywords: Flow matching, Safety guarantees, Planning and Control

Abstract: 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 \emph{SafeFlowMatcher}, a planning framework that couples FM with control barrier functions (CBFs) to achieve \emph{both} real-time efficiency and certified safety. SafeFlowMatcher uses a two-phase \emph{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 and locomotion. Extensive ablations corroborate the contributions of the PC integrator and the barrier certificate.

TL;DR: We propose SafeFlowMatcher, a novel method for safe and fast planning that couples flow matching with control barrier functions via a two-phase prediction–correction integrator