Robustness of Diffusion Models under Distribution Shift
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 19 of its 53 references that are in the map. First posted on arXiv 23 Sep 2026.
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19 of 53 references.
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- 2026On the Limits of Latent Reuse in Diffusion Models13 May
- 2026Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees10 Jan
- 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance5 Aug
- 2025DDPM Score Matching and Distribution Learning7 Apr
- 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models12 Mar
- 2025Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learning6 Feb
- 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
- 2024From optimal score matching to optimal sampling11 Sep
- 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
- 2024Learning general Gaussian mixtures with efficient score matching29 Apr
- 2024Learning Mixtures of Gaussians Using Diffusion Models29 Apr
- 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
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Other references · 5
- 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
- 2025Generalization error bound for denoising score matching under relaxed manifold assumptioncited by 18
- 2025Implicit score matching meets denoising score matching: improved rates of convergence and log-density Hessian estimationcited by 4
- 2026Generative models for decision-making under distributional shiftcited by 4
- 2025Guided Transfer Learning for Discrete Diffusion Modelscited by 3
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- 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
- 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
- 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
- 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions
- 2026Tightening the Score Matching Gap for Diffusion Models
- 2023Diffusion Models are Minimax Optimal Distribution Estimators
- 2025Low-dimensional adaptation of diffusion models: Convergence in total variation
- 2026On the Robustness of Langevin Dynamics to Score Function Error