Euclidean Distance-Based Flow Matching
Flow Matching has recently become popular as a technique for generative modeling with applications in many domains. In the standard Flow Matching formulation, we interpret the vector field as the solution of a least-squares regression problem, which is known to be sensitive to contamination. Therefore we leverage the viewpoint of robust statistics and replace the squared Euclidean distance with the Euclidean distance as a regression objective. This seemingly minor change strongly affects the properties of Flow Matching. We provide a probabilistic interpretation of the new regression target as a conditional geometric median and use this characterization to study distributional robustness o...
| Authors | Paul-Henrik Heilmann, Peter Ochs |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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