# Joint Non-Linear MRI Inversion with Diffusion Priors

arXiv: https://arxiv.org/abs/2310.14842 · HTML: https://mlsanity.com/paper/2310.14842/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 18 of its 28 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [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)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Models](https://mlsanity.com/paper/1903.12370/) (2019)
- [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)
- [Stable Deep MRI Reconstruction using Generative Priors](https://mlsanity.com/paper/2210.13834/) (2022)
- [Explicit Diffusion of Gaussian Mixture Model Based Image Priors](https://mlsanity.com/paper/2302.08411/) (2023)

## Built on by (most cited first, 2 of 2)

- [MotionDPS: Motion-Compensated 3D Brain MRI Reconstruction](https://mlsanity.com/paper/2605.22121/) (2026)
- [Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction](https://mlsanity.com/paper/2605.10629/) (2026)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven reconstruction approaches, in particular diffusion models, recently achieved remarkable success in reconstructing these data, but typically rely on estimating the coil sensitivities in an off-line step. This suffers from potential movement and misalignment artifacts and limits the application to Cartesian sampling trajectories. To obviate the need for off-line sensitivity estimation, we propose to jointly estimate the sensitivity maps with the image. In particular, we utilize a diffusion model -- trained on magnitude images only -- to generate high-fidelity images while imposing spatial smoothness of the sensitivity maps in the reverse diffusion. The proposed approach demonstrates consistent qualitative and quantitative performance across different sub-sampling patterns. In addition, experiments indicate a good fit of the estimated coil sensitivities.