mlsanityData to 7 Oct 2026

Monte Carlo guided Diffusion for Bayesian linear inverse problems

arXiv 2308.07983 ↗First posted 15 Aug 2023stat.ML cs.LG stat.MEcited by 65

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

Abstract (arXiv)

Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, MCGDiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.

Key facts. Cited by 65 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 30 of its 56 references that are in the map. First posted on arXiv 15 Aug 2023.

Builds on

30 of 56 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  2. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 28

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2016Density estimation using Real NVPcited by 2,029
  7. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  8. 2019An Introduction to Variational Autoencoderscited by 997
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  10. 2018Generative Image Inpainting with Contextual Attentioncited by 578
  11. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  12. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
16 more
  1. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  2. 2020A Review on Generative Adversarial Networks: Algorithms, Theory, and Applicationscited by 209
  3. 2019Pluralistic Image Completioncited by 162
  4. 2021High-Fidelity Pluralistic Image Completion with Transformerscited by 134
  5. 2021Generating Diverse Structure for Image Inpainting With Hierarchical VQ-VAEcited by 106
  6. 2021Aggregated Contextual Transformations for High-Resolution Image Inpaintingcited by 89
  7. 2018Variational Autoencoder with Arbitrary Conditioningcited by 68
  8. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  9. 2022From Denoising Diffusions to Denoising Markov Modelscited by 58
  10. 2017Deep Mean-Shift Priors for Image Restorationcited by 34
  11. 2020An invitation to sequential Monte Carlo samplerscited by 33
  12. 2022Semi-supervised Invertible Neural Operators for Bayesian Inverse Problemscited by 25
  13. 2021Deep Unfolding with Normalizing Flow Priors for Inverse Problemscited by 23
  14. 2016A Variational Bayesian Approach for Image Restoration. Application to Image Deblurring with Poisson-Gaussian Noisecited by 6
  15. 2023A domain-decomposed VAE method for Bayesian inverse problemscited by 6
  16. 2022Utilizing variational autoencoders in the Bayesian inverse problem of photoacoustic tomographycited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 14; 2025: 28; 2026: 22.

65 papers.

Sort:

By area:

  1. 2025A General Framework for Inference-time Scaling and Steering of Diffusion Modelscited by 201
  2. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  3. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  5. 2025Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Expertscited by 85
  6. 2025Inference-Time Alignment in Diffusion Models with Reward-Guided Generation: Tutorial and Reviewcited by 82
  7. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  8. 2024Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Designcited by 72
  9. 2024Particle Denoising Diffusion Samplercited by 63
  10. 2023Provable Probabilistic Imaging using Score-Based Generative Priorscited by 51
  11. 2025Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcingcited by 37
  12. 2025Dynamic Search for Inference-Time Alignment in Diffusion Modelscited by 36
38 more
  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  2. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  3. 2025Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Modelscited by 23
  4. 2025Reward-Guided Iterative Refinement in Diffusion Models at Test-Time with Applications to Protein and DNA Designcited by 21
  5. 2024Learning Image Priors through Patch-based Diffusion Models for Solving Inverse Problemscited by 18
  6. 2025CoDe: Blockwise Control for Denoising Diffusion Modelscited by 14
  7. 2024DiffusionBlend: Learning 3D Image Prior through Position-aware Diffusion Score Blending for 3D Computed Tomography Reconstructioncited by 13
  8. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 12
  9. 2026Decoupled Diffusion Sampling for Inverse Problems on Function Spacescited by 9
  10. 2025Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planningcited by 8
  11. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  12. 2025MIRA: Towards Mitigating Reward Hacking in Inference-Time Alignment of T2I Diffusion Modelscited by 7
  13. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  14. 2026Training-Free Adaptation of Diffusion Models via Doob's h-Transformcited by 6
  15. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Samplingcited by 5
  16. 2025Wasserstein Convergence of Critically Damped Langevin Diffusionscited by 5
  17. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  18. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIMcited by 4
  19. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  20. 2025A Recovery Theory for Diffusion Priors: Deterministic Analysis of the Implicit Prior Algorithmcited by 3
  21. 2025Controllable protein design with particle-based Feynman-Kac steeringcited by 3
  22. 2025DAPS++: Rethinking Diffusion Inverse Problems with Decoupled Posterior Annealingcited by 3
  23. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  24. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 3
  25. 2024Flow Matching for Posterior Inference with Simulator Feedbackcited by 2
  26. 2025Tree Reward-Aligned Search for TReASURe in Masked Diffusion Language Modelscited by 2
  27. 2025Local MAP Sampling for Diffusion Modelscited by 2
  28. 2025Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Samplingcited by 2
  29. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 2
  30. 2024Linearly Constrained Diffusion Implicit Modelscited by 1
  31. 2024Diffusion priors for Bayesian 3D reconstruction from incomplete measurementscited by 1
  32. 2025Injecting Measurement Information Yields a Fast and Noise-Robust Diffusion-Based Inverse Problem Solvercited by 1
  33. 2025Repulsive Monte Carlo on the sphere for the sliced Wasserstein distancecited by 1
  34. 2025Inverse problems with diffusion models: MAP estimation via mode-seeking losscited by 1
  35. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  36. 2026A Gibbs posterior sampler for inverse problem based on prior diffusion modelcited by 1
  37. 2026Diffusion Alignment Beyond KL: Variance Minimisation as Effective Policy Optimisercited by 1
  38. 2026Exact Posterior Score Estimation for Solving Linear Inverse Problemscited by 1

50 most cited of 65 All 65 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2025Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo
  2. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problems
  3. 2024Bayesian computation with generative diffusion models by Multilevel Monte Carlo
  4. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
  5. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
  6. 2023Score-based Diffusion Models for Bayesian Image Reconstruction
  7. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior
  8. 2025Diffusion models for inverse problems