mlsanityData to 7 Oct 2026

Split-and-augmented Gibbs sampler - Application to large-scale inference problems

arXiv 1804.05809 ↗First posted 16 Apr 2018stat.ME eess.SP stat.COcited by 47

Not on the map. Why?

Cited by 27 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction method of multipliers (ADMM) main steps. The proposed framework enables to derive faster and more efficient sampling schemes than the current state-of-the-art methods and can embed the latter. By sampling efficiently the parameter to infer as well as the hyperparameters of the problem, the generated samples can be used to approximate Bayesian estimators of the parameters to infer. Additionally, the proposed approach brings confidence intervals at a low cost contrary to optimization methods. Simulations on two often-studied signal processing problems illustrate the performance of the two proposed samplers. All results are compared to those obtained by recent state-of-the-art optimization and MCMC algorithms used to solve these problems.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Apr 2018.

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Citing papers per year: 2021: 1; 2022: 2; 2023: 3; 2024: 8; 2025: 17; 2026: 16.

47 papers.

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  1. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  2. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstructioncited by 73
  3. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  4. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  5. 2025Split Gibbs Discrete Diffusion Posterior Samplingcited by 18
  6. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  7. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimizationcited by 14
  8. 2021DG-LMC: A Turn-key and Scalable Synchronous Distributed MCMC Algorithm via Langevin Monte Carlo within Gibbscited by 11
  9. 2022The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distributioncited by 11
  10. 2024Regularization by denoising: Bayesian model and Langevin-within-split Gibbs samplingcited by 9
  11. 2024Empirical Bayesian image restoration by Langevin sampling with a denoising diffusion implicit priorcited by 6
  12. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Samplingcited by 6
35 more
  1. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion modelscited by 5
  2. 2023Machine Learning and the Future of Bayesian Computationcited by 4
  3. 2023Accelerated Bayesian imaging by relaxed proximal-point Langevin samplingcited by 4
  4. 2025DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networkscited by 4
  5. 2022Approximate blocked Gibbs sampling for Bayesian neural networkscited by 3
  6. 2025Super-Resolution Optical Coherence Tomography Using Diffusion Model-Based Plug-and-Play Priorscited by 3
  7. 2025Blade: A Derivative-free Bayesian Inversion Method using Diffusion Priorscited by 3
  8. 2025PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Priorcited by 3
  9. 2026Reward-Guided Discrete Diffusion via Clean-Sample Markov Chain for Molecule and Biological Sequence Designcited by 3
  10. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
  11. 2026Bayesian Uncertainty-Aware MRI Reconstructioncited by 3
  12. 2024Scalable Vertical Federated Learning via Data Augmentation and Amortized Inferencecited by 2
  13. 2025Plug-and-Play Posterior Sampling for Blind Inverse Problemscited by 2
  14. 2025LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restorationcited by 2
  15. 2026Dual-space posterior sampling for Bayesian inference in constrained inverse problemscited by 2
  16. 2025Noise Conditional Variational Score Distillationcited by 1
  17. 2025Diffusion-Prior Split Gibbs Sampling for Synthetic Aperture Radar Imaging under Incomplete Measurementscited by 1
  18. 2026Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Samplingcited by 1
  19. 2026Composing diffusion priors with explicit physical context via generative Gibbs samplingcited by 1
  20. 2024Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multiplierscited by 0
  21. 2024Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methodscited by 0
  22. 2024Provable Accuracy Bounds for Hybrid Dynamical Optimization and Samplingcited by 0
  23. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  24. 2025Clustering by Denoising: Latent plug-and-play diffusion for single-cell datacited by 0
  25. 2025Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problemscited by 0
  26. 2026Super-Resolution and Denoising of Corneal B-Scan OCT Imaging Using Diffusion Model Plug-and-Play Priorscited by 0
  27. 2026Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior samplingcited by 0
  28. 2026Dependency-Aware Discrete Diffusion for Scene Graph Generationcited by 0
  29. 2026Discrete Langevin-Inspired Posterior Samplingcited by 0
  30. 2026Bayesian Tensor Decomposition with Diffusion Model Priorcited by 0
  31. 2026Bridging data-driven priors via the score function for posterior sampling -- Comparative review and experimental studycited by 0
  32. 2026Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Modelscited by 0
  33. 2026Physical-State-Guided Diffusion Sampling for Full-Waveform Inversioncited by 0
  34. 2026FlowSGS: Improving Flow Matching Priors for Inverse Imaging with Stochastic Interpolantscited by 0
  35. 2026Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfoldingcited by 0