mlsanityData to 7 Oct 2026

Diffusion models for inverse problems

arXiv 2508.01975 ↗First posted 4 Aug 2025cs.LG stat.MLcited by 15

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

Abstract (arXiv)

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more classic explicit approximation approaches and others, which include variational inference, sequential monte carlo, and decoupled data consistency. We cover the extension to more challenging situations, including blind cases, high-dimensional data, and problems under data scarcity and distribution mismatch. More recent approaches that aim to leverage multimodal information through texts are covered. Through this chapter, we aim to (i) distill the common mathematical threads that connect these algorithms, (ii) systematically contrast their assumptions and performance trade-offs across representative inverse problems, and (iii) spotlight the open theoretical and practical challenges by clarifying the landscape of diffusion model based inverse problem solvers.

Key facts. Cited by 15 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 73 of its 92 references that are in the map. First posted on arXiv 4 Aug 2025.

Builds on

73 of 92 references.

Closest ancestors · 31

Same direction, newest first

  1. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior31 Jan
  2. 2025SILO: Solving Inverse Problems with Latent Operators20 Jan
  3. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems6 Oct
  4. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  5. 2024Amortized Posterior Sampling with Diffusion Prior Distillation25 Jul
  6. 2024Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems23 Jul
  7. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problems15 Jul
  8. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  9. 2024An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations1 Jul
  10. 2024Repulsive Latent Score Distillation for Solving Inverse Problems24 Jun
  11. 2024Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problems4 Jun
  12. 2024Learning Diffusion Priors from Observations by Expectation Maximization22 May
19 more
  1. 2024Diffusion Posterior Proximal Sampling for Image Restoration25 Feb
  2. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance3 Feb
  3. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  4. 2023Regularization by Texts for Latent Diffusion Inverse Solvers27 Nov
  5. 2023Prompt-tuning latent diffusion models for inverse problems2 Oct
  6. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior5 Sep
  7. 2023Fast Diffusion EM: a diffusion model for blind inverse problems with application to deconvolution1 Sep
  8. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  9. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  10. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  11. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  12. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  13. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems10 Mar
  14. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration30 Jan
  15. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problems19 Nov
  16. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  17. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  18. 2022Denoising Diffusion Restoration Models27 Jan
  19. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 42

  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. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2018Neural Ordinary Differential Equationscited by 3,733
  8. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  9. 2016Density estimation using Real NVPcited by 2,029
  10. 2023Consistency Modelscited by 1,778
  11. 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
  12. 2017Deep Image Priorcited by 1,097
30 more
  1. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  2. 2021Score-based Generative Modeling in Latent Spacecited by 634
  3. 2017The Perception-Distortion Tradeoffcited by 582
  4. 2017Compressed Sensing using Generative Modelscited by 337
  5. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  6. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  7. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  8. 2023I2SB: Image-to-Image Schr"odinger Bridgecited by 214
  9. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
  10. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  11. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  12. 2023Image Restoration with Mean-Reverting Stochastic Differential Equationscited by 182
  13. 2023Manifold Preserving Guided Diffusioncited by 153
  14. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 130
  15. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 110
  16. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  17. 2024Guidance with Spherical Gaussian Constraint for Conditional Diffusioncited by 69
  18. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 65
  19. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistentcited by 58
  20. 2023Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Modelscited by 53
  21. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  22. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  23. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  24. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  25. 2025Solving Inverse Problems with FLAIRcited by 16
  26. 2023Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstructioncited by 15
  27. 2020ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithmscited by 13
  28. 2025SteerX: Creating Any Camera-Free 3D and 4D Scenes with Geometric Steeringcited by 13
  29. 2025ContextMRI: Enhancing Compressed Sensing MRI through Metadata Conditioningcited by 8
  30. 2025Proxies for Distortion and Consistency with Applications for Real-World Image Restorationcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 7; 2026: 8.

15 papers.

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  1. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  2. 2025InverseCrafter: Efficient Video ReCapture as a Latent Domain Inverse Problemcited by 6
  3. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  4. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  5. 2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 4
  6. 2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 3
  7. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inferencecited by 1
  8. 2025Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithmcited by 0
  9. 2025UPMRI: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matchingcited by 0
  10. 2025AODDiff: Probabilistic Reconstruction of Aerosol Optical Depth via Diffusion-based Bayesian Inferencecited by 0
  11. 2026Likelihood-Separable Diffusion Inference for Multi-Image MRI Super-Resolutioncited by 0
  12. 2026Iterative Amortized Hierarchical VAEcited by 0
3 more
  1. 2026Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspectivecited by 0
  2. 2026A Principled Self-Referenced Early Stopping Approach for Deep Image Priorcited by 0
  3. 2026High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstructioncited by 0

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  2. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
  3. 2025SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problems
  4. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithm
  5. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  6. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealing
  7. 2025A Mixture-Based Framework for Guiding Diffusion Models
  8. 2023Accelerating Diffusion Models for Inverse Problems through Shortcut Sampling