mlsanityData to 7 Oct 2026

Deep Bayesian Inversion

arXiv 1811.05910 ↗First posted 14 Nov 2018stat.ML cs.LG math.STcited by 60

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Abstract (arXiv)

Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most realistic imaging applications in the clinic. We introduce two novel deep learning based methods for solving large-scale inverse problems using Bayesian inversion: a sampling based method using a WGAN with a novel mini-discriminator and a direct approach that trains a neural network using a novel loss function. The performance of both methods is demonstrated on image reconstruction in ultra low dose 3D helical CT. We compute the posterior mean and standard deviation of the 3D images followed by a hypothesis test to assess whether a "dark spot" in the liver of a cancer stricken patient is present. Both methods are computationally efficient and our evaluation shows very promising performance that clearly supports the claim that Bayesian inversion is usable for 3D imaging in time critical applications.

Key facts. Cited by 60 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Nov 2018.

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Citing papers per year: 2021: 10; 2022: 10; 2023: 19; 2024: 7; 2025: 7; 2026: 7.

60 papers.

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  1. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 78
  2. 2022Learned reconstruction methods with convergence guaranteescited by 46
  3. 2021Stochastic Image Denoising by Sampling from the Posterior Distributioncited by 45
  4. 2022GATSBI: Generative Adversarial Training for Simulation-Based Inferencecited by 36
  5. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  6. 2021High Perceptual Quality Image Denoising with a Posterior Sampling CGANcited by 33
  7. 2021Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priorscited by 29
  8. 2023Conditional Optimal Transport on Function Spacescited by 26
  9. 2022Reliable amortized variational inference with physics-based latent distribution correctioncited by 25
  10. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  11. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  12. 2022The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problemscited by 15
38 more
  1. 2021Wasserstein Patch Prior for Image Superresolutioncited by 13
  2. 2021Deep Bayesian inference for seismic imaging with taskscited by 12
  3. 2023Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problemscited by 12
  4. 2022The Inverse of Exact Renormalization Group Flows as Statistical Inferencecited by 11
  5. 2021Learning by example: fast reliability-aware seismic imaging with normalizing flowscited by 10
  6. 2023A Conditional Normalizing Flow for Accelerated Multi-Coil MR Imagingcited by 10
  7. 2022Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priorscited by 9
  8. 2022Computed Tomography Reconstruction using Generative Energy-Based Priorscited by 9
  9. 2022A Regularized Conditional GAN for Posterior Sampling in Image Recovery Problemscited by 9
  10. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  11. 2023Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantificationcited by 8
  12. 2024Task-Driven Uncertainty Quantification in Inverse Problems via Conformal Predictioncited by 8
  13. 2023Solution of physics-based inverse problems using conditional generative adversarial networks with full gradient penaltycited by 7
  14. 2023A generative flow for conditional sampling via optimal transportcited by 7
  15. 2024Nonlinear Assimilation via Score-based Sequential Langevin Samplingcited by 7
  16. 2024Conditional score-based diffusion models for solving inverse problems in mechanicscited by 6
  17. 2025Probing forced responses and causality in data-driven climate emulators: conceptual limitations and the role of reduced-order modelscited by 6
  18. 2023Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecastscited by 5
  19. 2023Deep Learning and Computational Physics (Lecture Notes)cited by 4
  20. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4
  21. 2023Refining Amortized Posterior Approximations using Gradient-Based Summary Statisticscited by 3
  22. 2023Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distancescited by 3
  23. 2021About exchanging expectation and supremum for conditional Wasserstein GANscited by 2
  24. 2022Trained Model in Supervised Deep Learning is a Conditional Risk Minimizercited by 2
  25. 2023Estimating Uncertainty in PET Image Reconstruction via Deep Posterior Samplingcited by 2
  26. 2024pcaGAN: Improving Posterior-Sampling cGANs via Principal Component Regularizationcited by 2
  27. 2025Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problemscited by 2
  28. 2025How many measurements are enough? Bayesian recovery in inverse problems with general distributionscited by 2
  29. 2025High Volume Rate 3D Ultrasound Reconstruction with Diffusion Modelscited by 2
  30. 2026An analytic theory of convolutional neural network inverse problems solverscited by 2
  31. 2026Dual-space posterior sampling for Bayesian inference in constrained inverse problemscited by 2
  32. 2021Classification and Uncertainty Quantification of Corrupted Data using Semi-Supervised Autoencoderscited by 1
  33. 2022Generative models and Bayesian inversion using Laplace approximationcited by 1
  34. 2023Uncertainty-Aware Null Space Networks for Data-Consistent Image Reconstructioncited by 1
  35. 2023Learning to sample in Cartesian MRIcited by 1
  36. 2024Integrating Generative and Physics-Based Models for Ptychographic Imaging with Uncertainty Quantificationcited by 1
  37. 2025Generative Algorithms for Wildfire Progression Reconstruction from Multi-Modal Satellite Active Fire Measurements and Terrain Heightcited by 1
  38. 2025An invertible generative model for forward and inverse problemscited by 1

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