Transport and flows between distributions over distributions

2024 | Powerpoint | PDF

Generative models based on transport, flows, and diffusion are widely deployed and usually connect a single source distribution to a single target distribution in Euclidean space. This talk covers the generalization when there are multiple source or target distributions, i.e., when the distributions are themselves over distributions. Transporting between many distributions arises in many applications, such as 1) text-to-image generation (each text prompt results in samples from a distribution over images), 2) image editing (between many pairs of images), 3) scheduling and supply-demand allocations (between many initial conditions) 4) point cloud generation (each point cloud is an empirical distribution), and 5) cellular transport (many pairs of untreated to treated populations). In this space, the talk will cover [Meta Optimal Transport](https://arxiv.org/abs/2206.05262) and [Meta Flow Matching](https://arxiv.org/abs/2408.14608) when the pairings or couplings between the distributions are known and otherwise [Wasserstein Flow Matching](https://arxiv.org/abs/2411.00698) over the Wasserstein manifold (using Riemannian Flow Matching) when there is no coupling information.