mlsanityData to 7 Oct 2026

Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors

arXiv 2403.11407 ↗First posted 18 Mar 2024stat.ML cs.LGcited by 28

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

Abstract (arXiv)

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors. Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample. Existing approaches to posterior sampling in this context address this problem either by retraining model-specific components, leading to stiff and cumbersome methods, or by introducing approximations with uncontrolled errors that affect the accuracy of the produced samples. We present an innovative framework, divide-and-conquer posterior sampling, which leverages the inherent structure of DDMs to construct a sequence of intermediate posteriors that guide the produced samples to the target posterior. Our method significantly reduces the approximation error associated with current techniques without the need for retraining. We demonstrate the versatility and effectiveness of our approach for a wide range of Bayesian inverse problems. The code is available at urlhttps://github.com/Badr-MOUFAD/dcps

Key facts. Cited by 28 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 35 of its 67 references that are in the map. First posted on arXiv 18 Mar 2024.

Builds on

35 of 67 references.

Closest ancestors · 6

Same direction, newest first

  1. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  2. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  3. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  5. 2022Denoising Diffusion Restoration Models27 Jan
  6. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 29

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  5. 2020Denoising Diffusion Implicit Modelscited by 9,655
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  7. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  8. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  9. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  10. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  11. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  12. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
17 more
  1. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  2. 2017Deep Image Priorcited by 1,097
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  4. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  5. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 303
  6. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  7. 2020Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulationcited by 225
  8. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  9. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 195
  10. 2022Stochastic Trajectory Prediction via Motion Indeterminacy Diffusioncited by 184
  11. 2020From Goals, Waypoints & Paths To Long Term Human Trajectory Forecastingcited by 166
  12. 2023Leapfrog Diffusion Model for Stochastic Trajectory Predictioncited by 129
  13. 2023Score-based Data Assimilationcited by 91
  14. 2022Subspace Diffusion Generative Modelscited by 70
  15. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  16. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  17. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 16; 2026: 8.

28 papers.

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By area:

  1. 2025Variational Control for Guidance in Diffusion Modelscited by 22
  2. 2025Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posteriorcited by 20
  3. 2024Conditional sampling within generative diffusion modelscited by 18
  4. 2025Solving Inverse Problems with FLAIRcited by 16
  5. 2025When Scores Learn Geometry: Rate Separations under the Manifold Hypothesiscited by 13
  6. 2024Posterior Sampling with Denoising Oracles via Tilted Transportcited by 12
  7. 2024Taming Diffusion Models for Image Restoration: A Reviewcited by 12
  8. 2025LanPaint: Training-Free Diffusion Inpainting with Asymptotically Exact and Fast Conditional Samplingcited by 11
  9. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlocited by 9
  10. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  11. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  12. 2025Diffusion models under low-noise regimecited by 5
16 more
  1. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  2. 2025Generative diffusion posterior sampling for informative likelihoodscited by 4
  3. 2026Calibrated Test-Time Guidance for Bayesian Inferencecited by 4
  4. 2025Local MAP Sampling for Diffusion Modelscited by 2
  5. 2026Image Restoration via Diffusion Models with Dynamic Resolutioncited by 2
  6. 2024Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beatcited by 1
  7. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate datacited by 1
  8. 2025Measurement-Aligned Sampling for Inverse Problemcited by 1
  9. 2025Inference-Time Search Using Side Information for Diffusion-Based Image Reconstructioncited by 1
  10. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  11. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  12. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  13. 2026Posterior Continuation with Noise-Conditioned Frequency Exposure for Diffusion Inverse Problemscited by 0
  14. 2026One step further with Monte-Carlo sampler to guide diffusion bettercited by 0
  15. 2026Hierarchical Variational Policies for Reward-Guided Diffusioncited by 0
  16. 2026Diffusion Editing with Soft Mask: Pixel Level Redo of Image and Video with Adjustable Strengthcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Mixture-Based Framework for Guiding Diffusion Models
  2. 2024Enhancing Diffusion Posterior Sampling for Inverse Problems by Integrating Crafted Measurements
  3. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
  4. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  5. 2026Sample-efficient evidence estimation of score based priors for model selection
  6. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  7. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems
  8. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach