mlsanityData to 7 Oct 2026

Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration

arXiv 2410.00418 ↗First posted 1 Oct 2024eess.IV cs.AI cs.CVcited by 32

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

Abstract (arXiv)

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods commonly attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the optimal estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

Key facts. Cited by 32 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 53 of its 66 references that are in the map. First posted on arXiv 1 Oct 2024.

Builds on

53 of 66 references.

Closest ancestors · 11

Same direction, newest first

  1. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  2. 2024FlowIE: Efficient Image Enhancement via Rectified Flow1 Jun
  3. 2023Towards Real-World Blind Face Restoration with Generative Diffusion Prior25 Dec
  4. 2023DiffBIR: Towards Blind Image Restoration with Generative Diffusion Prior29 Aug
  5. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  6. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  7. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration30 Jan
  8. 2022DifFace: Blind Face Restoration with Diffused Error Contraction13 Dec
  9. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  10. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  11. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 42

  1. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2016Image-to-Image Translation with Conditional Adversarial Networkscited by 4,510
  6. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  7. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  8. 2016Improved Techniques for Training GANscited by 2,938
  9. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  10. 2021SwinIR: Image Restoration Using Swin Transformercited by 1,869
  11. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
30 more
  1. 2018Demystifying MMD GANscited by 1,268
  2. 2018ESRGAN: Enhanced Super-Resolution Generative Adversarial Networkscited by 1,250
  3. 2016Colorful Image Colorizationcited by 1,113
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  5. 2021Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Datacited by 961
  6. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 925
  7. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  8. 2017The Perception-Distortion Tradeoffcited by 582
  9. 2021Designing a Practical Degradation Model for Deep Blind Image Super-Resolutioncited by 524
  10. 2017NIMA: Neural Image Assessmentcited by 387
  11. 2021Towards Real-World Blind Face Restoration with Generative Facial Priorcited by 347
  12. 2022Towards Robust Blind Face Restoration with Codebook Lookup Transformercited by 230
  13. 2022BBDM: Image-to-image Translation with Brownian Bridge Diffusion Modelscited by 222
  14. 2015Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networkscited by 214
  15. 2021GAN Prior Embedded Network for Blind Face Restoration in the Wildcited by 197
  16. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  17. 2017Real-Time User-Guided Image Colorization with Learned Deep Priorscited by 123
  18. 2022VQFR: Blind Face Restoration with Vector-Quantized Dictionary and Parallel Decodercited by 116
  19. 2024Scalable High-Resolution Pixel-Space Image Synthesis with Hourglass Diffusion Transformerscited by 116
  20. 2023Stochastic interpolants with data-dependent couplingscited by 94
  21. 2022RestoreFormer: High-Quality Blind Face Restoration from Undegraded Key-Value Pairscited by 85
  22. 2021A Theory of the Distortion-Perception Tradeoff in Wasserstein Spacecited by 52
  23. 2021Stochastic Image Denoising by Sampling from the Posterior Distributioncited by 45
  24. 2017Pixel Recursive Super Resolutioncited by 44
  25. 2021High Perceptual Quality Image Denoising with a Posterior Sampling CGANcited by 33
  26. 2023RestoreFormer++: Towards Real-World Blind Face Restoration from Undegraded Key-Value Pairscited by 33
  27. 2017PixColor: Pixel Recursive Colorizationcited by 32
  28. 2023Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restorationcited by 15
  29. 2022A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problemscited by 9
  30. 2022High-Perceptual Quality JPEG Decoding via Posterior Samplingcited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 17; 2026: 15.

32 papers.

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  1. 2025Compressed Image Generation with Denoising Diffusion Codebook Modelscited by 24
  2. 2025Efficient Image Restoration via Latent Consistency Flow Matchingcited by 8
  3. 2026Low Light Image Enhancement Challenge at NTIRE 2026cited by 7
  4. 2025Kernel Density Steering: Inference-Time Scaling via Mode Seeking for Image Restorationcited by 5
  5. 2025HazeMatching: Dehazing Light Microscopy Images with Guided Conditional Flow Matchingcited by 3
  6. 2025Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysiscited by 3
  7. 2026Prior-Informed Flow Matching for Graph Reconstructioncited by 3
  8. 2025Efficient Image Restoration with State-Dependent Forward Diffusioncited by 2
  9. 2025Flow Diverse and Efficient: Learning Momentum Flow Matching via Stochastic Velocity Field Samplingcited by 2
  10. 2025Unlocking the Potential of Diffusion Priors in Blind Face Restorationcited by 2
  11. 2026Contrast-X: A Multi-Modal Contrast Image Synthesis Benchmark and Universal Modality Flow Matchingcited by 2
  12. 2025Reconstruct Anything Model: a lightweight general model for computational imagingcited by 1
20 more
  1. 2025A Simple Combination of Diffusion Models for Better Quality Trade-Offs in Image Denoisingcited by 1
  2. 2025V.I.P. : Iterative Online Preference Distillation for Efficient Video Diffusion Modelscited by 1
  3. 2025Synthesizing Accurate and Realistic T1-weighted Contrast-Enhanced MR Images using Posterior-Mean Rectified Flowcited by 1
  4. 2025Regularized Schr"odinger Bridge via Distortion-Perception Perturbation for High-Fidelity Speech Enhancementcited by 1
  5. 2026SP3: Spherical Priors for Plug-and-Play Restorationcited by 1
  6. 2026Flow Straight to Reality: Perceptually Consistent Flow Matching for Efficient Image Restorationcited by 1
  7. 2025End-to-End PET Image Reconstruction via a Posterior-Mean Diffusion Modelcited by 0
  8. 2025On Inverse Problems, Parameter Estimation, and Domain Generalizationcited by 0
  9. 2025Latent Posterior-Mean Rectified Flow for Higher-Fidelity Perceptual Face Restorationcited by 0
  10. 2025Unsupervised Real-World Super-Resolution via Rectified Flow Degradation Modellingcited by 0
  11. 2026Categorical Reparameterization with Denoising Diffusion modelscited by 0
  12. 2026Optimizing ID Consistency in Multimodal Large Models: Facial Restoration via Alignment, Entanglement, and Disentanglementcited by 0
  13. 2026Linearized Coupling Flow with Shortcut Constraints for One-Step Face Restorationcited by 0
  14. 2026IR-Flow: Bridging Discriminative and Generative Image Restoration via Rectified Flowcited by 0
  15. 2026Flow-based Gaussian Splatting for Continuous-Scale Remote Sensing Image Super-Resolutioncited by 0
  16. 2026Resolving Endpoint Underfitting in Diffusion Bridges via Noise Alignmentcited by 0
  17. 2026DRIFT: Difficulty-aware Rectified Flows for Through-plane MRI Super-Resolutioncited by 0
  18. 2026Fast and Faithful: Principled Conditional Flow Matching for Inverse Problemscited by 0
  19. 2026Efficient 3D Whole-Body PET Image Denoising via Conditional Rectified Flow With Optimized Sampling Strategycited by 0
  20. 2026SolarFlowRefiner: Refinement-Aware Flow Matching for Surface Solar Radiation Downscalingcited by 0

Similar, not cited

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  1. 2026ScaleResfusion: Residual Rectified Flow based on Residual Vector Field
  2. 2025Reversing Flow for Image Restoration
  3. 2026Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems
  4. 2025Plug-and-Play Image Restoration with Flow Matching: A Continuous Viewpoint
  5. 2026ReBridge-Flow: Re-Coupling Posterior Bridges in Flow Matching for Image Restoration
  6. 2025Proxies for Distortion and Consistency with Applications for Real-World Image Restoration
  7. 2025Image Restoration via Primal Dual Hybrid Gradient and Flow Generative Model
  8. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matching