Promises and Pitfalls of Flow / Diffusion Models for Optimal Transport

Thornton James, Apple

Diffusion models; Schrödinger bridges and flow matching are interconnected paradigms which provide a promising new approach to high dimensional optimal transport. These methods leverage the scalability of modern generative models but may utilise data-to-data couplings for applications in various fields including inverse problems; text to speech; molecular dynamics, and single cell biology. The usefulness of these couplings depends on the choice of reference dynamics, and hence corresponding ground cost in the transport problem. There are however many common misunderstandings and open challenges remaining; in particular around applicability to general reference dynamics. This talk will introduce and contrast the relative merits of diffusion Schrödinger bridges and flow matching methods through the lens of reference dynamics, extension to the Riemannian manifold setting; and related computational challenges.

Area: IS6 - Generative modelling and stochastic mass transport (Giovanni Conforti)

Keywords: Diffusion Models

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