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PreprintarXiv licencearXiv

Generative bootstrap processes

  • Ziming Lin
  • Fang Han
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Abstract

We study generative bootstrap processes obtained by resampling from fitted generative distributions. We establish necessary and sufficient conditions for their conditional weak convergence to the P-Brownian bridge, formulated in terms of finite-dimensional conditional weak convergence and conditional asymptotic equicontinuity. We further provide general sufficient conditions and a Giné-Zinn-type characterization relating this convergence to the P-Donsker property. As applications, we verify these conditions for prominent classes of generative models, including triangular normalizing flows, flow matching, score-based diffusion models, and Wasserstein generative adversarial networks.

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Cite

BibTeXRIS
BibTeX
@misc{lin2026generative,
  title = {{Generative bootstrap processes}},
  author = {Ziming Lin and Fang Han},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13471},
  eprint = {2609.13471},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13471},
}
RIS
TY  - UNPB
TI  - Generative bootstrap processes
AU  - Ziming Lin
AU  - Fang Han
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13471
UR  - https://arxiv.org/abs/2609.13471
AB  - We study generative bootstrap processes obtained by resampling from fitted generative distributions. We establish necessary and sufficient conditions for their conditional weak convergence to the P-Brownian bridge, formulated in terms of finite-dimensional conditional weak convergence and conditional asymptotic equicontinuity. We further provide general sufficient conditions and a Giné-Zinn-type characterization relating this convergence to the P-Donsker property. As applications, we verify these conditions for prominent classes of generative models, including triangular normalizing flows, flow matching, score-based diffusion models, and Wasserstein generative adversarial networks.
ER  -