Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support
Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely treats ambient-space regularity or data supported exactly on low-dimensional sets. We study linear FM under a noisy latent-generator model, where a low-dimensional Hölder map is perturbed by nondegenerate ambient Gaussian noise, so the target law is full-dimensional despite its latent structure. We construct a spatially regular ReLU velocity class and establish non-asymptotic high-probability approximation and estimation bounds whose leading sample-size exponent is governed by the latent dimension rather than the ambient dimension, with ambien...
| Authors | Lifeng Hao, Shaolin Ji |
|---|---|
| Primary category | cs.LG |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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