Transfer of population robustness guarantees to trained models

Determine whether the theoretical robustness properties of the Euclidean-distance-based (L_{2,1}) Flow Matching population objective carry over to models trained with finite data, neural-network approximation, and nonzero optimization error.

Background

The paper’s theoretical results concern optimal population-level vector fields, while the experiments train neural networks using finite contaminated datasets and numerical optimization. Thus, the theoretical analysis does not directly account for statistical estimation, model approximation, or optimization effects.

The unresolved issue is whether the robustness observed and proved for the population minimizer persists in practically trained Flow Matching models under these sources of error.

References

A limitation of our results is that the theoretical results concern optimal vector fields at the population level. They do not account for estimation from finite data, approximation by neural networks, or optimization error. The extent to which the theoretical robustness properties carry over to trained models therefore remains unresolved.

— Euclidean Distance-Based Flow Matching  (2610.18534 - Heilmann et al., 13 Oct 2026) in Section 4, subsection “Discussion and Limitations”