Topological Flow Matching
Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance. However, its standard formulation treats signals on structured spaces, such as fMRI data on brain graphs, as points in Euclidean space, overlooking the rich topological features of their domains. To address this, we introduce topological flow matching, a topology-aware generalization of flow matching. We interpret flow matching as a framework for solving a degenerate Schrödinger bridge problem and inject topological information by augmenting the reference process with a Laplacian-derived drift. This principled modification captures the structure of the underlying domain w...
| Authors | Kacper Wyrwal, İsmail İlkan Ceylan, Alexander Tong |
|---|---|
| Primary category | cs.LG |
| Published | 14 June 2026 |
| Last updated at source | 14 June 2026 |
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