Robustness of Diffusion Models under Distribution Shift

2026-09-23

AI Summary

研究了在Wasserstein扰动下，扩散模型的鲁棒性问题，并通过分解统计成本和分布偏移成本提出了一种新的估计方法。

Abstract

Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution, yet existing theoretical guarantees largely focus on the no-shift setting. In this work, we study robust score estimation under Wasserstein perturbations of a reference distribution. For the Ornstein--Uhlenbeck diffusion, we show that robust estimation decomposes into two fundamental components: the statistical cost of learning the reference distribution and the intrinsic cost of distribution shift. The latter scales quadratically with the Wasserstein radius, and this dependence is minimax optimal. We construct an explicit finite-sample estimator achieving the resulting robust minimax rate without knowing the shift radius. When the reference distribution lies on an unknown low-dimensional subspace, the statistical term adapts to the intrinsic dimension while the shift cost remains unchanged. Finally, we show that the same decomposition governs positive-time reverse sampling and obtain matching minimax guarantees in KL divergence. Together, these results characterize how finite data, intrinsic dimension, and distribution shift affect the robustness of score-based diffusion models.

Problem

• Robustness
• Diffusion Models
• Distribution Shift
• Wasserstein Perturbations
• Score Estimation

Innovation

• Robust Score Estimation
• Wasserstein Perturbations
• Minimax Optimal
• Intrinsic Dimension
• Distribution Shift