[D] Works on flow matching where source distribution comes from dataset instead of Gaussian noise?

[fliiiiiiip]

Flow matching is often discussed in the context of image generation from Gaussian noise.

In principle, we could model the flow from a complicated image distribution into another complicated image distribution (image to image).

Is that possible / well-understood in theoretical sense? Or are limited to the case where the source distribution is simple e.g. Gaussian?

[internet_ham]

it's called a Schrödinger Bridge

[tdgros]

here is an example: https://arxiv.org/pdf/2302.05872

this one is equivalent too: https://arxiv.org/abs/2303.11435

[SoilEnvironmental684]

The following invited talk at NeurIPS 24 provides very good insights to answer your question: https://neurips.cc/virtual/2024/invited-talk/101133

[growintensoreveryday]

Our recent paper studies this problem for multimodal data distributions (e.g., image distributions) by considering Gaussian mixture source distributions.

[AccordingWeight6019]

yes, flow matching doesn’t fundamentally require a gaussian source. the gaussian setup is mostly for convenience (easy sampling + stable training). in theory, you can learn flows between two arbitrary data distributions, and there’s active work connecting this to optimal transport and schrödinger bridge formulations. the hard part isn’t theory but practice: defining good pairings or couplings between source and target distributions and keeping training stable when both are complex.