Generative bootstrap processes

Ziming Lin; Fang Han

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arXiv · 2609.13471

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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Ziming Lin, Fang Han. 2026-09-11. Generative bootstrap processes. https://arxiv.org/abs/2609.13471

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