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Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support — arXiv:2609.38918

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.38918
License (as archived): CC0-1.0
Archived: 2026-10-07T13:45:38.744Z
SHA-256 of the archived text: 96b8ab52832f7fa27876507b170b3a02e1c13d5e38c1b340b10d1abcced15f9e
Stable URL of this page: https://metraipolis.com/documento/dc_5ee257e51144

How to cite

Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support — arXiv:2609.38918 — arXiv (en), https://arxiv.org/abs/2609.38918 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5ee257e51144 (Metraipolis archive dc_5ee257e51144, sha256 96b8ab52832f7fa27876507b170b3a02e1c13d5e38c1b340b10d1abcced15f9e)

BibTeX

@misc{dc5ee257e51144,
  title = {Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support — arXiv:2609.38918},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38918},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5ee257e51144; sha256 96b8ab52832f7fa27876507b170b3a02e1c13d5e38c1b340b10d1abcced15f9e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38918. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 ambient and noise dependence kept explicit. Fixed positive target noise keeps the interpolation nondegenerate over the full time interval. The same spatial regularity propagates the learned velocity error through the transport ODE, yielding a corresponding Wasserstein convergence guarantee. These results show that exact low-dimensional support is not necessary for Flow Matching to retain latent-dimensional statistical behavior.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.38918 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T13:18:10.288Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).