mlsanityData to 7 Oct 2026

Think Twice Before You Act: Improving Inverse Problem Solving With MCMC

arXiv 2409.08551 ↗First posted 13 Sep 2024stat.ML cs.LGcited by 8

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

Abstract (arXiv)

Recent studies demonstrate that diffusion models can serve as a strong prior for solving inverse problems. A prominent example is Diffusion Posterior Sampling (DPS), which approximates the posterior distribution of data given the measure using Tweedie's formula. Despite the merits of being versatile in solving various inverse problems without re-training, the performance of DPS is hindered by the fact that this posterior approximation can be inaccurate especially for high noise levels. Therefore, we propose Diffusion Posterior MCMC (DPMC), a novel inference algorithm based on Annealed MCMC to solve inverse problems with pretrained diffusion models. We define a series of intermediate distributions inspired by the approximated conditional distributions used by DPS. Through annealed MCMC sampling, we encourage the samples to follow each intermediate distribution more closely before moving to the next distribution at a lower noise level, and therefore reduce the accumulated error along the path. We test our algorithm in various inverse problems, including super resolution, Gaussian deblurring, motion deblurring, inpainting, and phase retrieval. Our algorithm outperforms DPS with less number of evaluations across nearly all tasks, and is competitive among existing approaches.

Key facts. Cited by 8 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 48 of its 60 references that are in the map. First posted on arXiv 13 Sep 2024.

Builds on

48 of 60 references.

Closest ancestors · 11

Same direction, newest first

  1. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  2. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  3. 2023Direct Diffusion Bridge using Data Consistency for Inverse Problems31 May
  4. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  5. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  6. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  7. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  9. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  10. 2022Denoising Diffusion Restoration Models27 Jan
  11. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 37

  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. 2020Denoising Diffusion Implicit Modelscited by 9,655
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  9. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  10. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  11. 2022Scalable Diffusion Models with Transformerscited by 5,931
  12. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
25 more
  1. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  3. 2022Video Diffusion Modelscited by 2,280
  4. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  5. 2023Zero-1-to-3: Zero-shot One Image to 3D Objectcited by 1,483
  6. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  7. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  8. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  9. 2023MVDream: Multi-view Diffusion for 3D Generationcited by 928
  10. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  11. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  12. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  13. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  14. 2023Improved Techniques for Training Consistency Modelscited by 430
  15. 2024CAT3D: Create Anything in 3D with Multi-View Diffusion Modelscited by 425
  16. 2023ReconFusion: 3D Reconstruction with Diffusion Priorscited by 317
  17. 2021Score-based diffusion models for accelerated MRIcited by 308
  18. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  19. 2023Emu Video: Factorizing Text-to-Video Generation by Explicit Image Conditioningcited by 254
  20. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 244
  21. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 216
  22. 2016A Theory of Generative ConvNetcited by 174
  23. 2019Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Modelcited by 147
  24. 2020Improved Contrastive Divergence Training of Energy Based Modelscited by 127
  25. 2017Convergence of Langevin MCMC in KL-divergencecited by 86

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 2; 2026: 3.

8 papers.

  1. 2025Denoising Score Distillation: From Noisy Diffusion Pretraining to One-Step High-Quality Generationcited by 7
  2. 2024Understanding Galaxy Morphology Evolution Through Cosmic Time via Redshift Conditioned Diffusion Modelscited by 4
  3. 2024Unlocking the Potential of Text-to-Image Diffusion with PAC-Bayesian Theorycited by 2
  4. 2026Stitched Value Model for Diffusion Alignmentcited by 2
  5. 2024Linearly Constrained Diffusion Implicit Modelscited by 1
  6. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion modelcited by 1
  7. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observationcited by 1
  8. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing
  2. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
  3. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  4. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  5. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
  6. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  7. 2025Diffusion models for inverse problems
  8. 2026Discrete Langevin-Inspired Posterior Sampling