Correcting Source Mismatch in Flow Matching with Radial-Angular Transport
Flow Matching is typically built from Gaussian sources and Euclidean probability paths. For heavy-tailed or anisotropic data, however, a Gaussian source induces a structural mismatch already at the level of the radial distribution. We introduce \textit{Radial--Angular Flow Matching (RAFM)}, a framework that explicitly corrects this source mismatch within the standard simulation-free Flow Matching template. RAFM uses a source whose radial law matches that of the data and whose conditional angular distribution is uniform on the sphere, thereby removing the Gaussian radial mismatch by construction. This reduces the remaining transport problem to angular alignment, which leads naturally to co...
| Authors | Fouad Oubari, Mathilde Mougeot |
|---|---|
| Primary category | cs.LG |
| Published | 5 April 2026 |
| Last updated at source | 5 April 2026 |
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