mlsanityData to 7 Oct 2026

Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior

arXiv 2309.01949 ↗First posted 5 Sep 2023cs.CVcited by 16

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

Abstract (arXiv)

We propose a surrogate function for efficient yet principled use of score-based priors in Bayesian imaging. We consider ill-posed inverse imaging problems in which one aims for a clean image posterior given incomplete or noisy measurements. Since the measurements do not uniquely determine a true image, a prior is needed to constrain the solution space. Recent work turned score-based diffusion models into principled priors for solving ill-posed imaging problems by appealing to an ODE-based log-probability function. However, evaluating the ODE is computationally inefficient and inhibits posterior estimation of high-dimensional images. Our proposed surrogate prior is based on the evidence lower bound of a score-based diffusion model. We demonstrate the surrogate prior on variational inference for efficient approximate posterior sampling of large images. Compared to the exact prior in previous work, our surrogate accelerates optimization of the variational image distribution by at least two orders of magnitude. We also find that our principled approach gives more accurate posterior estimation than non-variational diffusion-based approaches that involve hyperparameter-tuning at inference. Our work establishes a practical path forward for using score-based diffusion models as general-purpose image priors.

Key facts. Cited by 16 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 43 of its 69 references that are in the map. First posted on arXiv 5 Sep 2023.

Builds on

43 of 69 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  2. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging23 Apr
  3. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration20 Mar
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  5. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraints2 Jun
  6. 2022Denoising Diffusion Restoration Models27 Jan
  7. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction9 Dec

Other references · 36

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Flow Matching for Generative Modelingcited by 5,426
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2018Neural Ordinary Differential Equationscited by 3,733
  8. 2014Deep Learning Face Attributes in the Wildcited by 3,679
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  10. 2023Consistency Modelscited by 1,778
  11. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  12. 2016Variational Inference: A Review for Statisticianscited by 1,466
24 more
  1. 2016Context Encoders: Feature Learning by Inpaintingcited by 1,424
  2. 2023Extracting Training Data from Diffusion Modelscited by 723
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  4. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  5. 2018Free-Form Image Inpainting with Gated Convolutioncited by 594
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  7. 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
  8. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  9. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  10. 2022Blended Latent Diffusioncited by 430
  11. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  12. 2021Score-based diffusion models for accelerated MRIcited by 308
  13. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  14. 2022Diffusion models as plug-and-play priorscited by 230
  15. 2023Understanding and Mitigating Copying in Diffusion Modelscited by 205
  16. 2022Towards the Detection of Diffusion Model Deepfakescited by 111
  17. 2018Adversarial Regularizers in Inverse Problemscited by 102
  18. 2022Deep Image Deblurring: A Surveycited by 94
  19. 2020Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imagingcited by 57
  20. 2020Learned convex regularizers for inverse problemscited by 54
  21. 2020Projected Distribution Loss for Image Enhancementcited by 29
  22. 2022Amortized Inference for Heterogeneous Reconstruction in Cryo-EMcited by 23
  23. 2020Extending LOUPE for K-space Under-sampling Pattern Optimization in Multi-coil MRIcited by 22
  24. 2022Posterior samples of source galaxies in strong gravitational lenses with score-based priorscited by 20

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 7; 2026: 3.

16 papers.

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  1. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  2. 2024Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matchingcited by 50
  3. 2025Diffusion models for inverse problemscited by 15
  4. 2024Integrating Amortized Inference with Diffusion Models for Learning Clean Distribution from Corrupted Imagescited by 12
  5. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7
  6. 2024Enhancing Diffusion Models for Inverse Problems with Covariance-Aware Posterior Samplingcited by 5
  7. 2024Score-Based Diffusion Models for Photoacoustic Tomography Image Reconstructioncited by 4
  8. 2023Bayesian Imaging for Radio Interferometry with Score-Based Priorscited by 3
  9. 2025STeP: A Framework for Solving Scientific Video Inverse Problems with Spatiotemporal Diffusion Priorscited by 3
  10. 2025Blind Strong Gravitational Lensing Inversion: Joint Inference of Source and Lens Mass with Score-Based Modelscited by 2
  11. 2025EquiReg: Equivariance Regularized Diffusion for Inverse Problemscited by 1
  12. 2025Diffusion models for multivariate subsurface generation and efficient probabilistic inversioncited by 1
4 more
  1. 2025Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inferencecited by 1
  2. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inferencecited by 1
  3. 2026ShuffleFlow: Scalable Posterior Inference for Bayesian Inverse Imagingcited by 1
  4. 2026Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
  2. 2026A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
  3. 2026Sample-efficient evidence estimation of score based priors for model selection
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors
  5. 2026Optimizing Diffusion Priors in Image Reconstruction from a Single Observation
  6. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  7. 2023Score-based Diffusion Models for Bayesian Image Reconstruction
  8. 2024Variational Diffusion Posterior Sampling with Midpoint Guidance