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Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching — arXiv:2611.01559

Source

arXiv (en)

Original

https://arxiv.org/abs/2611.01559

License (as archived)

CC0-1.0

Archived

2026-11-03T10:47:42.256Z

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95e7b737b70664e6f50ee9a86a9be1704f672e667a545432e379ea136adc9e3b

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Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching — arXiv:2611.01559 — arXiv (en), https://arxiv.org/abs/2611.01559 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f75ed3401a67 (Metraipolis archive dc_f75ed3401a67, sha256 95e7b737b70664e6f50ee9a86a9be1704f672e667a545432e379ea136adc9e3b)

@misc{dcf75ed3401a67,
  title = {Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching — arXiv:2611.01559},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01559},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f75ed3401a67; sha256 95e7b737b70664e6f50ee9a86a9be1704f672e667a545432e379ea136adc9e3b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01559. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Flow matching has emerged as a promising alternative to diffusion-based generative modeling, offering a continuous-time ordinary differential equation formulation with fast sampling and a simple regression-based training objective. Despite its empirical success, some theoretical analyses idealize the learning procedure by assuming that the velocity field is obtained by exact empirical risk minimization. This assumption does not reflect the practical finite-dataset setting, where the empirical flow-matching loss is only approximately minimized by a finite number of stochastic-gradient updates. We develop an empirical-risk-minimizer-free analysis for flow matching that explicitly accounts for both finite-sample statistical error and finite-time empirical optimization error. Our analysis considers a finite dataset of \(N\) flow-matching samples and a learned parameter \(\theta_T\) obtained after \(T\) stochastic gradient updates on the empirical objective. Under regularity assumptions on the interpolation path, sub-exponential source and target distributions, approximation by a bounded-parameter smooth neural velocity class, empirical-loss optimization, and uniform flow stability, we prove a guarantee that holds with high probability over the finite training dataset and in expectation over the stochastic-gradient randomness. The resulting bound separates approximation error, statistical error from the finite dataset, tail error from unbounded source and target distributions, and empirical optimization error from approximate minimization of the finite-sample objective.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2611.01559 — 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 2026-11-03T10:39:50.486Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).