# Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models

arXiv: https://arxiv.org/abs/2202.01479 · HTML: https://mlsanity.com/paper/2202.01479/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 3 Feb 2022.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 17 of 17)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [MRI Reconstruction Using Deep Bayesian Estimation](https://mlsanity.com/paper/1909.01127/) (2019)
- [XPDNet for MRI Reconstruction: an application to the 2020 fastMRI challenge](https://mlsanity.com/paper/2010.07290/) (2020)

## Built on by (most cited first, 30 of 47)

- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [A review of uncertainty quantification in medical image analysis: probabilistic and non-probabilistic methods](https://mlsanity.com/paper/2310.06873/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction](https://mlsanity.com/paper/2309.00783/) (2023)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [The Emergence of Reproducibility and Generalizability in Diffusion Models](https://mlsanity.com/paper/2310.05264/) (2023)
- [MRI Reconstruction with Side Information using Diffusion Models](https://mlsanity.com/paper/2303.14795/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [Self-Supervised Adversarial Diffusion Models for Fast MRI Reconstruction](https://mlsanity.com/paper/2406.15656/) (2024)
- [Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI](https://mlsanity.com/paper/2403.05245/) (2024)
- [Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]](https://mlsanity.com/paper/2502.01358/) (2025)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Investigating the Adversarial Robustness of Density Estimation Using the Probability Flow ODE](https://mlsanity.com/paper/2310.07084/) (2023)
- [Autoregressive Image Diffusion: Generation of Image Sequence and Application in MRI](https://mlsanity.com/paper/2405.14327/) (2024)
- [INFusion: Diffusion Regularized Implicit Neural Representations for 2D and 3D accelerated MRI reconstruction](https://mlsanity.com/paper/2406.13895/) (2024)
- [Robust multi-coil MRI reconstruction via self-supervised denoising](https://mlsanity.com/paper/2411.12919/) (2024)
- [Antithetic Noise in Diffusion Models](https://mlsanity.com/paper/2506.06185/) (2025)
- [Self-diffusion for Solving Inverse Problems](https://mlsanity.com/paper/2510.21417/) (2025)
- [PixCUE: Joint Uncertainty Estimation and Image Reconstruction in MRI using Deep Pixel Classification](https://mlsanity.com/paper/2303.00111/) (2023)
- [Generative Priors for MRI Reconstruction Trained from Magnitude-Only Images Using Phase Augmentation](https://mlsanity.com/paper/2308.02340/) (2023)
- [Denoising Diffusion Probabilistic Models for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/2410.23318/) (2024)
- [Joint Non-Linear MRI Inversion with Diffusion Priors](https://mlsanity.com/paper/2310.14842/) (2023)
- [Robust Simultaneous Multislice MRI Reconstruction Using Slice-Wise Learned Generative Diffusion Priors](https://mlsanity.com/paper/2407.21600/) (2024)
- [Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction](https://mlsanity.com/paper/2411.03758/) (2024)
- [Fast MRI for All: Bridging Access Gaps by Training without Raw Data](https://mlsanity.com/paper/2411.13022/) (2024)

## Abstract (arXiv)

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method. In addition to the maximum a posteriori (MAP) estimate for the image, which can be obtained with conventional methods, the minimum mean square error (MMSE) estimate and uncertainty maps can also be computed. The data-driven Markov chains are constructed from the generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. This provides flexibility because the method can be applied to k-space acquired with different sampling schemes or receive coils using the same pre-trained models. Furthermore, we use a framework based on a reverse diffusion process to be able to utilize advanced generative models. The performance of the method is evaluated on an open dataset using 10-fold undersampling in k-space.