Diffusion Bootstrap for High-Dimensional Linear Models

Ce Liang; Wei Ma

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arXiv · 2607.24324

Diffusion Bootstrap for High-Dimensional Linear Models

Ce Liang·Wei Ma

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Abstract

Classical bootstrap methods can behave poorly in high-dimensional linear models: the pairs bootstrap often yields overly conservative inference, whereas the residual bootstrap can be anti-conservative, reflecting systematic failures in variance calibration. We propose a diffusion-based pairs bootstrap that replaces the empirical joint distribution with a learned generative law. We establish variance consistency under a score approximation assumption, using complementary SDE and PDE arguments. Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency. Experiments indicate that diffusion pairs bootstrap improves variance calibration and generally improves Type~I error calibration, including in settings not covered by our theory.

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Ce Liang, Wei Ma. 2026-07-27. Diffusion Bootstrap for High-Dimensional Linear Models. https://arxiv.org/abs/2607.24324

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