aiqbench analysis
This research establishes theoretical bounds for the robustness of score-based diffusion models when faced with distribution shifts, specifically quantifying how estimation error scales quadratically with the magnitude of the perturbation. By decomposing the statistical cost into components related to intrinsic dimension and shift radius, the study provides minimax-optimal estimators that function without prior knowledge of the shift extent. These findings are critical for advancing the reliability of generative AI systems in real-world applications where training and deployment data distributions inevitably diverge.
Robustness of Diffusion Models under Distribution Shift
arXiv:2609.27546v1 Announce Type: cross 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.
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.
Statistics Theory (math.ST); Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML)
arXiv:2609.27546 [math.ST]
(or arXiv:2609.27546v1 [math.ST] for this version)
https://doi.org/10.48550/arXiv.2609.27546 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 268 words
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