# Stable Deep MRI Reconstruction using Generative Priors

arXiv: https://arxiv.org/abs/2210.13834 · HTML: https://mlsanity.com/paper/2210.13834/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 61 references that are in the map.
- First posted on arXiv 25 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (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)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Relating Adversarially Robust Generalization to Flat Minima](https://mlsanity.com/paper/2104.04448/) (2021)
- [Total Deep Variation for Linear Inverse Problems](https://mlsanity.com/paper/2001.05005/) (2020)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [Model Learning: Primal Dual Networks for Fast MR imaging](https://mlsanity.com/paper/1908.02426/) (2019)
- [Invert to Learn to Invert](https://mlsanity.com/paper/1911.10914/) (2019)
- [Deep variational network for rapid 4D flow MRI reconstruction](https://mlsanity.com/paper/2004.09610/) (2020)
- [Computed Tomography Reconstruction using Generative Energy-Based Priors](https://mlsanity.com/paper/2203.12658/) (2022)
- [MRI Reconstruction Using Deep Energy-Based Model](https://mlsanity.com/paper/2109.03237/) (2021)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)

## Built on by (most cited first, 21 of 21)

- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [Learning Regularization Functionals for Inverse Problems: A Comparative Study](https://mlsanity.com/paper/2510.01755/) (2025)
- [Robustness of Deep Learning for Accelerated MRI: Benefits of Diverse Training Data](https://mlsanity.com/paper/2312.10271/) (2023)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Product of Gaussian Mixture Diffusion Models](https://mlsanity.com/paper/2310.12653/) (2023)
- [Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]](https://mlsanity.com/paper/2502.01358/) (2025)
- [DEALing with Image Reconstruction: Deep Attentive Least Squares](https://mlsanity.com/paper/2502.04079/) (2025)
- [Autoregressive Image Diffusion: Generation of Image Sequence and Application in MRI](https://mlsanity.com/paper/2405.14327/) (2024)
- [Joint Non-Linear MRI Inversion with Diffusion Priors](https://mlsanity.com/paper/2310.14842/) (2023)
- [Bigger Isn't Always Better: Towards a General Prior for Medical Image Reconstruction](https://mlsanity.com/paper/2501.07376/) (2025)
- [Conformal Bounds on Full-Reference Image Quality for Imaging Inverse Problems](https://mlsanity.com/paper/2505.09528/) (2025)
- [How many measurements are enough? Bayesian recovery in inverse problems with general distributions](https://mlsanity.com/paper/2505.10630/) (2025)
- [Interpretable Similarity of Synthetic Image Utility](https://mlsanity.com/paper/2512.17080/) (2025)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Guiding Quantitative MRI Reconstruction with Phase-wise Uncertainty](https://mlsanity.com/paper/2502.20877/) (2025)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [Exploiting Intermediate Reconstructions in Optical Coherence Tomography for Test-Time Adaption of Medical Image Segmentation](https://mlsanity.com/paper/2603.05041/) (2026)
- [Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction](https://mlsanity.com/paper/2603.27158/) (2026)
- [MotionDPS: Motion-Compensated 3D Brain MRI Reconstruction](https://mlsanity.com/paper/2605.22121/) (2026)
- [Outlier Detection Using Generative Models with Theoretical Performance Guarantees](https://mlsanity.com/paper/2310.09999/) (2023)
- [Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction](https://mlsanity.com/paper/2605.10629/) (2026)

## Abstract (arXiv)

Data-driven approaches recently achieved remarkable success in magnetic resonance imaging (MRI) reconstruction, but integration into clinical routine remains challenging due to a lack of generalizability and interpretability. In this paper, we address these challenges in a unified framework based on generative image priors. We propose a novel deep neural network based regularizer which is trained in a generative setting on reference magnitude images only. After training, the regularizer encodes higher-level domain statistics which we demonstrate by synthesizing images without data. Embedding the trained model in a classical variational approach yields high-quality reconstructions irrespective of the sub-sampling pattern. In addition, the model shows stable behavior when confronted with out-of-distribution data in the form of contrast variation. Furthermore, a probabilistic interpretation provides a distribution of reconstructions and hence allows uncertainty quantification. To reconstruct parallel MRI, we propose a fast algorithm to jointly estimate the image and the sensitivity maps. The results demonstrate competitive performance, on par with state-of-the-art end-to-end deep learning methods, while preserving the flexibility with respect to sub-sampling patterns and allowing for uncertainty quantification.