mlsanityData to 14 Oct 2026

Variational Diffusion Posterior Sampling with Midpoint Guidance

arXiv 2410.09945 ↗First posted 13 Oct 2024stat.ML cs.LGcited by 32

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

Abstract (arXiv)

Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable terms. To tackle this issue, state-of-the-art approaches formulate the problem as that of sampling from a surrogate diffusion model targeting the posterior and decompose its scores into two terms: the prior score and an intractable guidance term. While the former is replaced by the pre-trained score of the considered diffusion model, the guidance term has to be estimated. In this paper, we propose a novel approach that utilises a decomposition of the transitions which, in contrast to previous methods, allows a trade-off between the complexity of the intractable guidance term and that of the prior transitions. We validate the proposed approach through extensive experiments on linear and nonlinear inverse problems, including challenging cases with latent diffusion models as priors. We then demonstrate its applicability to various modalities and its promising impact on public health by tackling cardiovascular disease diagnosis through the reconstruction of incomplete electrocardiograms. The code is publicly available at urlhttps://github.com/yazidjanati/mgps.

Key facts. Cited by 32 papers in the map (data through 14 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 41 of its 61 references that are in the map. First posted on arXiv 13 Oct 2024.

Builds on

41 of 61 references.

Closest ancestors · 9

Same direction, newest first

  1. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems15 Aug
  2. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency16 Jul
  3. 2023Solving Linear Inverse Problems Provably via Posterior Sampling with Latent Diffusion Models2 Jul
  4. 2023Denoising Diffusion Models for Plug-and-Play Image Restoration15 May
  5. 2023A Variational Perspective on Solving Inverse Problems with Diffusion Models7 May
  6. 2023Removing Structured Noise with Diffusion Models20 Jan
  7. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model1 Dec
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep
  9. 2022Denoising Diffusion Restoration Models27 Jan

Other references · 32

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  4. 2020Denoising Diffusion Implicit Modelscited by 9,781
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  8. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,013
  9. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  10. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  11. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  12. 2022Video Diffusion Modelscited by 2,305
20 more
  1. 2021Image Super-Resolution via Iterative Refinementcited by 1,511
  2. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,430
  3. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 635
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  5. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 236
  6. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 232
  7. 2023MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusioncited by 213
  8. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  9. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 197
  10. 2021SNIPS: Solving Noisy Inverse Problems Stochasticallycited by 191
  11. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  12. 2020Deep Learning for ECG Analysis: Benchmarks and Insights from PTB-XLcited by 158
  13. 2023Score-based Data Assimilationcited by 96
  14. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 79
  15. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 64
  16. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  17. 2021Explore Image Deblurring via Blur Kernel Spacecited by 58
  18. 2023Diffusion-based Conditional ECG Generation with Structured State Space Modelscited by 36
  19. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
  20. 2023Image Inpainting via Tractable Steering of Diffusion Modelscited by 22

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 20; 2026: 11.

32 papers.

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  1. 2025Solving Inverse Problems with FLAIRcited by 17
  2. 2025LATINO-PRO: LAtent consisTency INverse sOlver with PRompt Optimizationcited by 16
  3. 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
  4. 2025InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problemscited by 10
  5. 2025Inverse Problem Sampling in Latent Space Using Sequential Monte Carlocited by 7
  6. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  7. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion modelscited by 6
  8. 2025Wasserstein Convergence of Critically Damped Langevin Diffusionscited by 6
  9. 2025ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problemscited by 5
  10. 2025PnP-CM: Consistency Models as Plug-and-Play Priors for Inverse Problemscited by 5
  11. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
  12. 2026Sample-efficient evidence estimation of score based priors for model selectioncited by 3
20 more
  1. 2024VIPaint: Image Inpainting with Pre-Trained Diffusion Models via Variational Inferencecited by 2
  2. 2025Greed is Good: A Unifying Perspective on Guided Generationcited by 2
  3. 2025LVTINO: LAtent Video consisTency INverse sOlver for High Definition Video Restorationcited by 2
  4. 2026Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stabilitycited by 2
  5. 2026Consistency Regularised Gradient Flows for Inverse Problemscited by 2
  6. 2026Image Restoration via Diffusion Models with Dynamic Resolutioncited by 2
  7. 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate datacited by 1
  8. 2025Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regionscited by 1
  9. 2025SAIP: A Plug-and-Play Scale-adaptive Module in Diffusion-based Inverse Problemscited by 1
  10. 2025Inverse problems with diffusion models: MAP estimation via mode-seeking losscited by 1
  11. 2026Outlier-robust Diffusion Posterior Sampling for Bayesian Inverse Problemscited by 1
  12. 2026Fast and Robust Likelihood-Guided Diffusion Posterior Sampling with Amortized Variational Inferencecited by 1
  13. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  14. 2026What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport Viewcited by 1
  15. 2026A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priorscited by 1
  16. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  17. 2025Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurementscited by 0
  18. 2025SURE Guided Posterior Sampling: Trajectory Correction for Diffusion-Based Inverse Problemscited by 0
  19. 2026Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priorscited by 0
  20. 2026Direct Conditional Transition Sampling for Diffusion Inverse Problemscited by 0

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  1. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  2. 2023Variational Bayesian Imaging with an Efficient Surrogate Score-based Prior
  3. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
  4. 2025A Mixture-Based Framework for Guiding Diffusion Models
  5. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imaging
  6. 2024Posterior Sampling with Denoising Oracles via Tilted Transport
  7. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  8. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEs