Stochastic Interpolations, Lipschitz Mass Transportation and Generative Learning

We construct a unit-time flow on the Euclidean space via stochastic interpolations, which unified recent ODE flows in generative learning. We study the well-posedness of the flow and establish the Lipschitz property of the flow map at time 1. We apply the Lipschitz mapping to several rich classes of probability measures on deriving functional inequalities with dimension-free constants, sampling and generative learning.

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