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Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental study

arXiv 2606.14800 ↗First posted 11 Jun 2026stat.ME cs.LG eess.IVcited by 0

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Abstract (arXiv)

This paper reviews how a diverse set of popular data-driven priors commonly used in Bayesian inverse problems can be unified through their respective score functions. By framing these priors under this common perspective, we show that they can benefit from their straightfoward and effective integration into a recently proposed sampling algorithm. The applicability of this common framework is illustrated by considering several data-driven priors, namely regularization-by-denoising, normalizing flow-based priors, score-based generative models, and convex-ridge regularizers. For these four particular priors, the performance of the method is evaluated when conducting image inpainting and single image super-resolution. These results, as well as those obtained when restoring real images acquired in a geological context, demonstrate the efficiency of the method. This unified framework proves versatile enough to handle any posterior distribution defined by a broad class of score function-based priors, beyond the specific cases considered in this paper.

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References · 37

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  6. 2018Neural Ordinary Differential Equationscited by 3,779
  7. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  8. 2020Plug-and-Play Image Restoration with Deep Denoiser Priorcited by 470
  9. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 340
  10. 2017Compressed Sensing using Generative Modelscited by 339
  11. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  12. 2018Analysis of Langevin Monte Carlo via convex optimizationcited by 127
25 more
  1. 2018Log-concave sampling: Metropolis-Hastings algorithms are fastcited by 118
  2. 2018Regularization by Denoising: Clarifications and New Interpretationscited by 103
  3. 2021Bayesian imaging using Plug & Play priors: when Langevin meets Tweediecited by 97
  4. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 97
  5. 2016Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreaucited by 84
  6. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  7. 2013Proximal Markov chain Monte Carlo algorithmscited by 46
  8. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 42
  9. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 41
  10. 2020Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithmcited by 35
  11. 2024Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learningcited by 35
  12. 2021Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithmscited by 24
  13. 2023Generative Plug and Play: Posterior Sampling for Inverse Problemscited by 24
  14. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  15. 2017Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methodscited by 13
  16. 2022Posterior-Variance-Based Error Quantification for Inverse Problems in Imagingcited by 12
  17. 2023Subgradient Langevin Methods for Sampling from Non-smooth Potentialscited by 11
  18. 2024Regularization by denoising: Bayesian model and Langevin-within-split Gibbs samplingcited by 9
  19. 2019Asymptotically exact data augmentation: models, properties and algorithmscited by 8
  20. 2023Normalizing flow sampling with Langevin dynamics in the latent spacecited by 7
  21. 2021Regularization via deep generative models: an analysis point of viewcited by 5
  22. 2024Plug-and-Play Priors as a Score-Based Methodcited by 5
  23. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  24. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4
  25. 2022Generative models and Bayesian inversion using Laplace approximationcited by 1

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