mlsanityData to 14 Oct 2026

Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data

arXiv 2403.08728 ↗First posted 13 Mar 2024cs.CV cs.AI cs.LGcited by 32

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

Abstract (arXiv)

We provide a framework for solving inverse problems with diffusion models learned from linearly corrupted data. Firstly, we extend the Ambient Diffusion framework to enable training directly from measurements corrupted in the Fourier domain. Subsequently, we train diffusion models for MRI with access only to Fourier subsampled multi-coil measurements at acceleration factors R= 2,4,6,8. Secondly, we propose Ambient Diffusion Posterior Sampling (A-DPS), a reconstruction algorithm that leverages generative models pre-trained on one type of corruption (e.g. image inpainting) to perform posterior sampling on measurements from a different forward process (e.g. image blurring). For MRI reconstruction in high acceleration regimes, we observe that A-DPS models trained on subsampled data are better suited to solving inverse problems than models trained on fully sampled data. We also test the efficacy of A-DPS on natural image datasets (CelebA, FFHQ, and AFHQ) and show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 41 of its 59 references that are in the map. First posted on arXiv 13 Mar 2024.

Builds on

41 of 59 references.

Closest ancestors · 6

Same direction, newest first

  1. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data2 May
  2. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  3. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  5. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  6. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 35

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  3. 2023Extracting Training Data from Diffusion Modelscited by 732
  4. 2018Noise2Noise: Learning Image Restoration without Clean Datacited by 533
  5. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 521
  6. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  7. 2022Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Modelscited by 424
  8. 2017MoDL: Model Based Deep Learning Architecture for Inverse Problemscited by 387
  9. 2018Noise2Void - Learning Denoising from Single Noisy Imagescited by 364
  10. 2017Learning a Variational Network for Reconstruction of Accelerated MRI Datacited by 342
  11. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  12. 2022Diffusion models as plug-and-play priorscited by 231
23 more
  1. 2023Fast Training of Diffusion Models with Masked Transformerscited by 176
  2. 2019Noisier2Noise: Learning to Denoise from Unpaired Noisy Datacited by 126
  3. 2018Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networkscited by 120
  4. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 113
  5. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 111
  6. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 74
  7. 2014From Denoising to Compressed Sensingcited by 68
  8. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  9. 2021Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurementscited by 56
  10. 2022SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluationcited by 44
  11. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  12. 2022A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noisecited by 30
  13. 2022Sensing Theorems for Unsupervised Learning in Linear Inverse Problemscited by 28
  14. 2022Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstructioncited by 23
  15. 2022Stable Deep MRI Reconstruction using Generative Priorscited by 21
  16. 2022Unsupervised Learning From Incomplete Measurements for Inverse Problemscited by 20
  17. 2023Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurringcited by 14
  18. 2023A Restoration Network as an Implicit Priorcited by 13
  19. 2023AmbientFlow: Invertible generative models from incomplete, noisy measurementscited by 11
  20. 2022A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problemscited by 9
  21. 2023FastMRI Prostate: A Publicly Available, Biparametric MRI Dataset to Advance Machine Learning for Prostate Cancer Imagingcited by 9
  22. 2023Image Reconstruction without Explicit Priorscited by 8
  23. 2023K-band: Self-supervised MRI Reconstruction via Stochastic Gradient Descent over K-space Subsetscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 16; 2026: 10.

32 papers.

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  1. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  2. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
  3. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  4. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  5. 2024Constrained Diffusion with Trust Samplingcited by 10
  6. 2025Measurement Score-Based Diffusion Modelcited by 8
  7. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  8. 2025DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximizationcited by 6
  9. 2025Inverse Flow and Consistency Modelscited by 5
  10. 2026Self-Supervised Learning from Noisy and Incomplete Datacited by 5
  11. 2024Robust multi-coil MRI reconstruction via self-supervised denoisingcited by 4
  12. 2025Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstructioncited by 4
20 more
  1. 2026Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performancecited by 4
  2. 2025DiffDenoise: Self-Supervised Medical Image Denoising with Conditional Diffusion Modelscited by 3
  3. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problemscited by 3
  4. 2025UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weightscited by 3
  5. 2024Fast MRI for All: Bridging Access Gaps by Training without Raw Datacited by 2
  6. 2025Learning Single Index Models with Diffusion Priorscited by 2
  7. 2025ADG: Ambient Diffusion-Guided Dataset Recovery for Corruption-Robust Offline Reinforcement Learningcited by 2
  8. 2026Ambient Dataloops: Generative Models for Dataset Refinementcited by 2
  9. 2025UPMRI: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matchingcited by 1
  10. 2026Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Datacited by 1
  11. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observationcited by 1
  12. 2025Measurement Score-Based MRI Reconstruction with Automatic Coil Sensitivity Estimationcited by 0
  13. 2025Patch-Based Diffusion for Data-Efficient, Radiologist-Preferred MRI Reconstructioncited by 0
  14. 2025Extendable Generalization Self-Supervised Diffusion for Low-Dose CT Reconstructioncited by 0
  15. 2025Robust Super-Capacity SRS Channel Inpainting via Diffusion Modelscited by 0
  16. 2026Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Modelscited by 0
  17. 2026SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posteriorcited by 0
  18. 2026Measurement Geometry and Design for Trustworthy Generative Inverse Problemscited by 0
  19. 2026Consistency Models for Fast MRI Reconstruction Using Regularization by Denoisingcited by 0
  20. 2026GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priorscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  2. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction
  3. 2025Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
  4. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models
  5. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  6. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
  7. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
  8. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency