mlsanityData to 7 Oct 2026

Solving Linear-Gaussian Bayesian Inverse Problems with Decoupled Diffusion Sequential Monte Carlo

arXiv 2502.06379 ↗First posted 10 Feb 2025cs.LG cs.AI stat.MLcited by 9

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

Abstract (arXiv)

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian inverse problems which builds on "decoupled diffusion", where the generative process is designed such that larger updates to the sample are possible. The method is asymptotically exact and we demonstrate the effectiveness of our Decoupled Diffusion Sequential Monte Carlo (DDSMC) algorithm on both synthetic as well as protein and image data. Further, we demonstrate how the approach can be extended to discrete data.

Key facts. Cited by 9 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 36 of its 56 references that are in the map. First posted on arXiv 10 Feb 2025.

Builds on

36 of 56 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  2. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  3. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors18 Mar
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  5. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  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. 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. 2022Classifier-Free Diffusion Guidancecited by 5,717
  12. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
19 more
  1. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  2. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  3. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  4. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  5. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  6. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 437
  7. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  8. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  9. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  10. 2022Continuous diffusion for categorical datacited by 202
  11. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  12. 2022Score-based Continuous-time Discrete Diffusion Modelscited by 167
  13. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Modelscited by 98
  14. 2013A Deep and Tractable Density Estimatorcited by 67
  15. 2019Elements of Sequential Monte Carlocited by 60
  16. 2024Conditional sampling within generative diffusion modelscited by 18
  17. 2023Correcting Diffusion Generation through Resamplingcited by 15
  18. 2024Solving Inverse Problems in Protein Space Using Diffusion-Based Priorscited by 13
  19. 2023Discriminator Guidance for Autoregressive Diffusion Modelscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 5.

9 papers.

  1. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  2. 2025ESS-Flow: Training-free guidance of flow-based models as inference in source spacecited by 6
  3. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matchingcited by 5
  4. 2025Generative diffusion posterior sampling for informative likelihoodscited by 4
  5. 2026Particle-Guided Diffusion Models for Partial Differential Equationscited by 4
  6. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate datacited by 1
  7. 2026Modelling Gas-Phase Reaction Kinetics with Guided Particle Diffusion Samplingcited by 0
  8. 2026Backward SDEs-based Diffusion for Physics-Constrained Generationcited by 0
  9. 2026Interacting particle guidance for sampling reward-tilted generative priorscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems
  2. 2024Bayesian computation with generative diffusion models by Multilevel Monte Carlo
  3. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlo
  4. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey
  5. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributions
  6. 2025Preconditioned Langevin Dynamics with Score-Based Generative Models for Infinite-Dimensional Linear Bayesian Inverse Problems
  7. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
  8. 2025Diffusion models for inverse problems