Stable Mean Flow: Lyapunov-Inspired One-Step Flow Matching

The Mean Flow Matching algorithm is the state-of-the-art for one-step generative models. Building on this idea, we propose the Stable Mean Flow algorithm and introduce a Lyapunov-inspired stability regularizer that enforces local non-expansivity of the single-step transport map. This design guarantees uniqueness of characteristics and bounds trajectory drift. We conduct experiments that show improved output quality and convergence speed over Mean Flow. Moreover, we establish explicit upper bounds on error growth for both one-step and multi-step generation.