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PreprintarXiv licencearXiv

Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees

  • Marta Gentiloni Silveri
  • Giovanni Conforti
  • Alain Durmus
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Abstract

Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.

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Cite

BibTeXRIS
BibTeX
@misc{silveri2026diffusion,
  title = {{Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees}},
  author = {Marta Gentiloni Silveri and Giovanni Conforti and Alain Durmus},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.16610},
  eprint = {2606.16610},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.16610},
}
RIS
TY  - UNPB
TI  - Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guarantees
AU  - Marta Gentiloni Silveri
AU  - Giovanni Conforti
AU  - Alain Durmus
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.16610
UR  - https://arxiv.org/abs/2606.16610
AB  - Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.
ER  -