mlsanityData to 14 Oct 2026

Fast and Robust Diffusion Posterior Sampling for MR Image Reconstruction Using the Preconditioned Unadjusted Langevin Algorithm

arXiv 2512.05791 ↗First posted 5 Dec 2025physics.med-ph cs.CV cs.LGcited by 0

On the map: Diffusion models → Medical imaging and segmentation

Abstract (arXiv)

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as diffusion posterior sampling (DPS) or likelihood annealing suffer from long reconstruction times and the need for parameter tuning. The purpose of this work is to develop a robust sampling algorithm with fast convergence. Theory and Methods: In the reverse diffusion process used for sampling the posterior, the exact likelihood is multiplied with the diffused prior at all noise scales. To overcome the issue of slow convergence, preconditioning is used. The method is trained on fastMRI data and tested on retrospectively undersampled brain data of a healthy volunteer. Results: For posterior sampling in Cartesian and non-Cartesian accelerated MRI the new approach outperforms annealed sampling and DPS in terms of reconstruction speed and sample quality. Conclusion: The proposed exact likelihood with preconditioning enables rapid and reliable posterior sampling across various MRI reconstruction tasks without the need for parameter tuning.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models. Builds on 18 of its 38 references that are in the map. First posted on arXiv 5 Dec 2025.

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18 of 38 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Accelerated Motion Correction with Deep Generative Diffusion Models1 Nov
  2. 2022Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models3 Feb
  3. 2021Score-based diffusion models for accelerated MRI8 Oct

Other references · 15

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  6. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  7. 2022Denoising Diffusion Restoration Modelscited by 963
  8. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  9. 2014Theoretical guarantees for approximate sampling from smooth and log-concave densitiescited by 208
  10. 2024A Survey on Diffusion Models for Inverse Problemscited by 180
  11. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 132
  12. 2025Diffusion models for inverse problemscited by 16
3 more
  1. 2019Preconditioned P-ULA for Joint Deconvolution-Segmentation of Ultrasound Images -- Extended Versioncited by 5
  2. 2022Deep, Deep Learning with BARTcited by 4
  3. 2024Bayesian Conditioned Diffusion Models for Inverse Problemscited by 2

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  1. 2025Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data
  2. 2023Optimizing Sampling Patterns for Compressed Sensing MRI with Diffusion Generative Models
  3. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstruction
  4. 2026Annealed Langevin Posterior Sampling (ALPS): A Rapid Algorithm for Image Restoration with Multiscale Energy Models
  5. 2026Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping
  6. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  7. 2025Posterior Sampling by Combining Diffusion Models with Annealed Langevin Dynamics
  8. 2025Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models