mlsanityData to 14 Oct 2026

Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey

arXiv 2510.14114 ↗First posted 15 Oct 2025cs.LGcited by 0

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

Abstract (arXiv)

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage pre-trained diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a twisting mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 42 of its 64 references that are in the map. First posted on arXiv 15 Oct 2025.

Builds on

42 of 64 references.

Closest ancestors · 14

Same direction, newest first

  1. 2025A Mixture-Based Framework for Guiding Diffusion Models5 Feb
  2. 2024Variational Diffusion Posterior Sampling with Midpoint Guidance13 Oct
  3. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  4. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMC13 Sep
  5. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Images15 Jul
  6. 2024Posterior Sampling with Denoising Oracles via Tilted Transport30 Jun
  7. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  8. 2024Learning Diffusion Priors from Observations by Expectation Maximization22 May
  9. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  10. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors18 Mar
  11. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  12. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
2 more
  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 28

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Denoising Diffusion Implicit Modelscited by 9,781
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  7. 2022Video Diffusion Modelscited by 2,305
  8. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  9. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,430
  10. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  11. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  12. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
16 more
  1. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  2. 2023MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusioncited by 213
  3. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 197
  4. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 136
  5. 2023Score-based Data Assimilationcited by 96
  6. 2024Particle Denoising Diffusion Samplercited by 65
  7. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 64
  8. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  9. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  10. 2020An invitation to sequential Monte Carlo samplerscited by 33
  11. 2017The Tamed Unadjusted Langevin Algorithmcited by 31
  12. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
  13. 2020Bayesian Image Reconstruction using Deep Generative Modelscited by 29
  14. 2022Variational Deep Image Restorationcited by 24
  15. 2024Conditional sampling within generative diffusion modelscited by 19
  16. 2022Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomographycited by 5

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  3. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo
  4. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  5. 2023Accelerating Markov Chain Monte Carlo sampling with diffusion models
  6. 2025Unifying and extending Diffusion Models through PDEs for solving Inverse Problems
  7. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion models
  8. 2026Leveraging generative models to assist Monte Carlo sampling