An aspect of flow matching which I find a bit interesting is that it is covariant under affine changes of coordinate (c.f. optimal transport, which need not be). This allows for a few nice WLOGs, which I imagine have more applications than I realise.
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Gabriel Peyré
Optimal transport computes an interpolation between two distributions using an optimal coupling. Flow matching, on the other hand, uses a simpler “independent” coupling, which is the product of the marginals.
Comments
Do you have an example or reference for OT not being covariant under affine coordinate changes?