# Product of Gaussian Mixture Diffusion Model for non-linear MRI Inversion

arXiv: https://arxiv.org/abs/2501.08662 · HTML: https://mlsanity.com/paper/2501.08662/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 0 of its 29 references that are in the map.
- First posted on arXiv 15 Jan 2025.

## Placed in

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

## Built on by (most cited first, 1 of 1)

- [Product-of-Gaussian-Mixture Diffusion Models for Joint Nonlinear MRI Reconstruction](https://mlsanity.com/paper/2605.10629/) (2026)

## Abstract (arXiv)

Diffusion models have recently shown remarkable results in magnetic resonance imaging reconstruction. However, the employed networks typically are black-box estimators of the (smoothed) prior score with tens of millions of parameters, restricting interpretability and increasing reconstruction time. Furthermore, parallel imaging reconstruction algorithms either rely on off-line coil sensitivity estimation, which is prone to misalignment and restricting sampling trajectories, or perform per-coil reconstruction, making the computational cost proportional to the number of coils. To overcome this, we jointly reconstruct the image and the coil sensitivities using the lightweight, parameter-efficient, and interpretable product of Gaussian mixture diffusion model as an image prior and a classical smoothness priors on the coil sensitivities. The proposed method delivers promising results while allowing for fast inference and demonstrating robustness to contrast out-of-distribution data and sampling trajectories, comparable to classical variational penalties such as total variation. Finally, the probabilistic formulation allows the calculation of the posterior expectation and pixel-wise variance.