mlsanityData to 7 Oct 2026

Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing

arXiv 2407.01521 ↗First posted 1 Jul 2024cs.LG cs.AI cs.CVcited by 157

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

Abstract (arXiv)

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems.

Key facts. Cited by 157 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 45 of its 60 references that are in the map. First posted on arXiv 1 Jul 2024.

Builds on

45 of 60 references.

Closest ancestors · 14

Same direction, newest first

  1. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  2. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  3. 2023Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion1 Dec
  4. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems15 Aug
  5. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  6. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  7. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  8. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  9. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  10. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  11. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems20 Nov
  12. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
2 more
  1. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  2. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  8. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  9. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  11. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  12. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
19 more
  1. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  2. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  3. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  4. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  5. 2023Analyzing and Improving the Training Dynamics of Diffusion Modelscited by 396
  6. 2021Score-based diffusion models for accelerated MRIcited by 308
  7. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  8. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  9. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  10. 2022Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imagingcited by 94
  11. 2023Conditional Diffusion Models for Semantic 3D Brain MRI Synthesiscited by 85
  12. 2022MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusioncited by 66
  13. 2021Explore Image Deblurring via Blur Kernel Spacecited by 58
  14. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  15. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  16. 2013Hamiltonian Monte Carlo for Hierarchical Modelscited by 50
  17. 2022PyTorch Image Quality: Metrics for Image Quality Assessmentcited by 34
  18. 2021Deep J-Sense: Accelerated MRI Reconstruction via Unrolled Alternating Optimizationcited by 19
  19. 2023Improved Diffusion-based Image Colorization via Piggybacked Modelscited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 63; 2026: 84.

157 papers.

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  1. 2024PnP-Flow: Plug-and-Play Image Restoration with Flow Matchingcited by 92
  2. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  3. 2025FlowDPS: Flow-Driven Posterior Sampling for Inverse Problemscited by 65
  4. 2024Sequential Controlled Langevin Diffusionscited by 47
  5. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  6. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 25
  7. 2024SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problemscited by 23
  8. 2025Flower: A Flow-Matching Solver for Inverse Problemscited by 23
  9. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 20
  10. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  11. 2025Solving Inverse Problems with FLAIRcited by 16
  12. 2025Diffusion models for inverse problemscited by 15
38 more
  1. 2024Diffusion State-Guided Projected Gradient for Inverse Problemscited by 14
  2. 2025Residual Diffusion Bridge Model for Image Restorationcited by 14
  3. 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
  4. 2024PostEdit: Posterior Sampling for Efficient Zero-Shot Image Editingcited by 9
  5. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 9
  6. 2025InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problemscited by 9
  7. 2026Decoupled Diffusion Sampling for Inverse Problems on Function Spacescited by 9
  8. 2025Multiscale guidance of protein structure prediction with heterogeneous cryo-EM datacited by 8
  9. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  10. 2025Steering Generative Models with Experimental Data for Protein Fitness Optimizationcited by 7
  11. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  12. 2025Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problemscited by 6
  13. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  14. 2025ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problemscited by 5
  15. 2025Test-Time Anchoring for Discrete Diffusion Posterior Samplingcited by 5
  16. 2025FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solverscited by 5
  17. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  18. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  19. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generationcited by 5
  20. 2024G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solvingcited by 4
  21. 2025Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolationcited by 4
  22. 2026Weak Diffusion Priors Can Still Achieve Strong Inverse-Problem Performancecited by 4
  23. 2026Calibrated Test-Time Guidance for Bayesian Inferencecited by 4
  24. 2026ProjFlow: Projection Sampling with Flow Matching for Zero-Shot Exact Spatial Motion Controlcited by 4
  25. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  26. 2025Dual Ascent Diffusion for Inverse Problemscited by 3
  27. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  28. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealingcited by 3
  29. 2025DAISI: Data Assimilation with Inverse Sampling using Stochastic Interpolantscited by 3
  30. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  31. 2024VIPaint: Image Inpainting with Pre-Trained Diffusion Models via Variational Inferencecited by 2
  32. 2025Greed is Good: A Unifying Perspective on Guided Generationcited by 2
  33. 2025Benchmarking Diffusion Annealing-Based Bayesian Inverse Problem Solverscited by 2
  34. 2025Learning Single Index Models with Diffusion Priorscited by 2
  35. 2025Diffusion prior as a direct regularization term for FWIcited by 2
  36. 2025Local MAP Sampling for Diffusion Modelscited by 2
  37. 2025Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Samplingcited by 2
  38. 2025Noise is All You Need: Solving Linear Inverse Problems by Noise Combination Sampling with Diffusion Modelscited by 2

50 most cited of 157 All 157 (JSON)

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  1. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMC
  2. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  3. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  4. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM
  5. 2025Diffusion Models for Solving Inverse Problems via Posterior Sampling with Piecewise Guidance
  6. 2024Diffusion Prior-Based Amortized Variational Inference for Noisy Inverse Problems
  7. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
  8. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Sampling