Flow matching ODE trajectories are shown to become attracted to the data mean, then to clusters, and then to converge at the terminal time under weak geometric assumptions, including submanifold-supported data.
Proof of Theorem C.6.By multiplying the integrating factorekt, we have that d ektyt dt =e kt d yt dt +ke ktyt ≤ϕ(t)e kt
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Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries and Denoisers
Flow matching ODE trajectories are shown to become attracted to the data mean, then to clusters, and then to converge at the terminal time under weak geometric assumptions, including submanifold-supported data.