mlsanityData to 7 Oct 2026

Unsupervised Detection of Distribution Shift in Inverse Problems using Diffusion Models

arXiv 2505.11482 ↗First posted 16 May 2025cs.CVcited by 4

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Diffusion models are widely used as priors in imaging inverse problems. However, their performance often degrades under distribution shifts between the training and test-time images. Existing methods for identifying and quantifying distribution shifts typically require access to clean test images, which are almost never available while solving inverse problems (at test time). We propose a fully unsupervised metric for estimating distribution shifts using only indirect (corrupted) measurements and score functions from diffusion models trained on different datasets. We theoretically show that this metric estimates the KL divergence between the training and test image distributions. Empirically, we show that our score-based metric, using only corrupted measurements, closely approximates the KL divergence computed from clean images. Motivated by this result, we show that aligning the out-of-distribution score with the in-distribution score -- using only corrupted measurements -- reduces the KL divergence and leads to improved reconstruction quality across multiple inverse problems.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 64 of its 74 references that are in the map. First posted on arXiv 16 May 2025.

Builds on

64 of 74 references.

Closest ancestors · 7

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  2. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems15 Jul
  3. 2024Detecting Out-Of-Distribution Earth Observation Images with Diffusion Models19 Apr
  4. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Survey18 Aug
  5. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  7. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 57

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  8. 2016A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networkscited by 2,362
  9. 2014Unsupervised Domain Adaptation by Backpropagationcited by 1,906
  10. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,366
  11. 2017Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networkscited by 1,325
  12. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
38 more
  1. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  2. 2022Diffusion Models in Vision: A Surveycited by 1,008
  3. 2021Generalized Out-of-Distribution Detection: A Surveycited by 796
  4. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  5. 2021Score-based Generative Modeling in Latent Spacecited by 634
  6. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  7. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  8. 2020Measuring Robustness to Natural Distribution Shifts in Image Classificationcited by 452
  9. 2019Contrastive Adaptation Network for Unsupervised Domain Adaptationcited by 407
  10. 2015Return of Frustratingly Easy Domain Adaptationcited by 389
  11. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 340
  12. 2021Score-based diffusion models for accelerated MRIcited by 308
  13. 2020A Brief Review of Domain Adaptationcited by 287
  14. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  15. 2021Exploring the Limits of Out-of-Distribution Detectioncited by 283
  16. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Surveycited by 269
  17. 2022OpenOOD: Benchmarking Generalized Out-of-Distribution Detectioncited by 267
  18. 2023Generalization in diffusion models arises from geometry-adaptive harmonic representationscited by 179
  19. 2021A Fine-Grained Analysis on Distribution Shiftcited by 171
  20. 2021A Unified Survey on Anomaly, Novelty, Open-Set, and Out-of-Distribution Detection: Solutions and Future Challengescited by 154
  21. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 130
  22. 2022Is Out-of-Distribution Detection Learnable?cited by 109
  23. 2022Denoising diffusion models for out-of-distribution detectioncited by 102
  24. 2021Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Taskscited by 100
  25. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Modelscited by 98
  26. 2023On Diffusion Modeling for Anomaly Detectioncited by 71
  27. 2022Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstructioncited by 64
  28. 2023Unsupervised Out-of-Distribution Detection with Diffusion Inpaintingcited by 57
  29. 2021Mandoline: Model Evaluation under Distribution Shiftcited by 55
  30. 2019Transfer Adaptation Learning: A Decade Surveycited by 52
  31. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  32. 2022Test-Time Training Can Close the Natural Distribution Shift Performance Gap in Deep Learning Based Compressed Sensingcited by 37
  33. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  34. 2022Towards Explaining Distribution Shiftscited by 26
  35. 2022DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removalcited by 25
  36. 2023DiffGuard: Semantic Mismatch-Guided Out-of-Distribution Detection using Pre-trained Diffusion Modelscited by 25
  37. 2023Synthetic ECG Signal Generation using Probabilistic Diffusion Modelscited by 22
  38. 2024Out-of-Distribution Detection with a Single Unconditional Diffusion Modelcited by 22

50 most cited of 57 All 57 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 2.

4 papers.

  1. 2025EigenScore: OOD Detection using Covariance in Diffusion Modelscited by 4
  2. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  3. 2025Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurementscited by 0
  4. 2026KLIP: localized distribution shift detection via KL-divergence with diffusion priors in Inverse Problemscited by 0

Similar, not cited

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  3. 2025Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching
  4. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems
  5. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging
  6. 2025Diffusion models for inverse problems
  7. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
  8. 2023DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistency