  Human motion synthesis is a fundamental task in computer animation. Recent
methods based on diffusion models or GPT structure demonstrate commendable
performance but exhibit drawbacks in terms of slow sampling speeds and error
accumulation. In this paper, we propose \emph{Motion Flow Matching}, a novel
generative model designed for human motion generation featuring efficient
sampling and effectiveness in motion editing applications. Our method reduces
the sampling complexity from thousand steps in previous diffusion models to
just ten steps, while achieving comparable performance in text-to-motion and
action-to-motion generation benchmarks. Noticeably, our approach establishes a
new state-of-the-art Fr\'echet Inception Distance on the KIT-ML dataset. What
is more, we tailor a straightforward motion editing paradigm named
\emph{sampling trajectory rewriting} leveraging the ODE-style generative models
and apply it to various editing scenarios including motion prediction, motion
in-between prediction, motion interpolation, and upper-body editing. Our code
will be released.
