When do explicit penalties improve flow matching?
Flow matching can learn structure directly from data, raising the question of when additional constraints improve generation. We study penalties that encode such constraints, with physics-informed flow matching as a motivating example. Satisfying a constraint more closely need not make the generated distribution more accurate. We therefore compare penalised and unpenalised generative modelling through their expected squared $2$-Wasserstein error. Our analysis covers both vector-valued and functional data in a Hilbert-space setting. We first derive geometric criteria that account for constraint violations and the distribution of samples after projection onto the constraint set. We then sol...
| Authors | Lea Kunkel, Alberto González-Sanz, Sophie Langer |
|---|---|
| Primary category | stat.ML |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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