mlsanityData to 7 Oct 2026

Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models

arXiv 2307.00619 ↗First posted 2 Jul 2023cs.LG cs.AI stat.MLcited by 156

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

Abstract (arXiv)

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Key facts. Cited by 156 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 47 of its 58 references that are in the map. First posted on arXiv 2 Jul 2023.

Builds on

47 of 58 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  2. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  3. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  4. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  5. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  6. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  7. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 40

  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. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,131
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2021LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairscited by 1,544
  9. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  10. 2016Context Encoders: Feature Learning by Inpaintingcited by 1,424
  11. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
28 more
  1. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  2. 2020Encoding in Style: a StyleGAN Encoder for Image-to-Image Translationcited by 727
  3. 2023DataComp: In search of the next generation of multimodal datasetscited by 635
  4. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  5. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  6. 2023AudioLDM: Text-to-Audio Generation with Latent Diffusion Modelscited by 592
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  8. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  9. 2017Compressed Sensing using Generative Modelscited by 337
  10. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  11. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  12. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  13. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noisecited by 275
  14. 2022Brain Imaging Generation with Latent Diffusion Modelscited by 267
  15. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  16. 2022Imagen Editor and EditBench: Advancing and Evaluating Text-Guided Image Inpaintingcited by 229
  17. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  18. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
  19. 2022Soft Diffusion: Score Matching for General Corruptionscited by 101
  20. 2019Coherent Semantic Attention for Image Inpaintingcited by 97
  21. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimationcited by 95
  22. 2019DeepRED: Deep Image Prior Powered by REDcited by 84
  23. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 73
  24. 2021Instance-Optimal Compressed Sensing via Posterior Samplingcited by 43
  25. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  26. 2023A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Modelscited by 37
  27. 2021Fairness for Image Generation with Uncertain Sensitive Attributescited by 31
  28. 2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 60; 2025: 55; 2026: 32.

156 papers.

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By area:

  1. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  2. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  3. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  4. 2023Manifold Preserving Guided Diffusioncited by 153
  5. 2024CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Modelscited by 138
  6. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 115
  7. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  8. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusioncited by 78
  9. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  10. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  11. 2023Training-free Linear Image Inverses via Flowscited by 70
  12. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
38 more
  1. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 65
  2. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  3. 2024Marigold-DC: Zero-Shot Monocular Depth Completion with Guided Diffusioncited by 47
  4. 2024RB-Modulation: Training-Free Personalization of Diffusion Models using Stochastic Optimal Controlcited by 46
  5. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  6. 2024Steering Rectified Flow Models in the Vector Field for Controlled Image Generationcited by 38
  7. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  8. 2024SplatFlow: Multi-View Rectified Flow Model for 3D Gaussian Splatting Synthesiscited by 34
  9. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  10. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  11. 2023Regularization by Texts for Latent Diffusion Inverse Solverscited by 31
  12. 2024Conditional Image Synthesis with Diffusion Models: A Surveycited by 29
  13. 20233DGR-CT: Sparse-View CT Reconstruction with a 3D Gaussian Representationcited by 24
  14. 2024You Only Need One Step: Fast Super-Resolution with Stable Diffusion via Scale Distillationcited by 23
  15. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problemscited by 23
  16. 2024DreamSampler: Unifying Diffusion Sampling and Score Distillation for Image Manipulationcited by 22
  17. 2024Warped Diffusion: Solving Video Inverse Problems with Image Diffusion Modelscited by 21
  18. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 20
  19. 2025Training-Free Constrained Generation With Stable Diffusion Modelscited by 20
  20. 2024Ensemble Kalman Diffusion Guidance: A Derivative-free Method for Inverse Problemscited by 18
  21. 2025SILO: Solving Inverse Problems with Latent Operatorscited by 18
  22. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  23. 2024Fast Samplers for Inverse Problems in Iterative Refinement Modelscited by 17
  24. 2025Solving Inverse Problems with FLAIRcited by 16
  25. 2024Bracket Diffusion: HDR Image Generation by Consistent LDR Denoisingcited by 15
  26. 2024Repulsive Latent Score Distillation for Solving Inverse Problemscited by 15
  27. 2024MoE-DiffIR: Task-customized Diffusion Priors for Universal Compressed Image Restorationcited by 15
  28. 2025Diffusion models for inverse problemscited by 15
  29. 2024Diffusion Posterior Proximal Sampling for Image Restorationcited by 14
  30. 2024Diffusion State-Guided Projected Gradient for Inverse Problemscited by 14
  31. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimizationcited by 14
  32. 2024VISION-XL: High Definition Video Inverse Problem Solver using Latent Image Diffusion Modelscited by 13
  33. 2024Invertible Diffusion Models for Compressed Sensingcited by 12
  34. 2024Automated Black-box Prompt Engineering for Personalized Text-to-Image Generationcited by 12
  35. 2024OmniSSR: Zero-shot Omnidirectional Image Super-Resolution using Stable Diffusion Modelcited by 11
  36. 2024Blind Inversion using Latent Diffusion Priorscited by 10
  37. 2023Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Modelscited by 9
  38. 2024Text-guided Explorable Image Super-resolutioncited by 9

50 most cited of 156 All 156 (JSON)

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  1. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling
  2. 2025Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Models
  3. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models
  4. 2023Removing Structured Noise with Diffusion Models
  5. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
  6. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  7. 2026SNaP: One-Step Posterior Sampling for Noisy Inverse Problems
  8. 2024Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance