# Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models

arXiv: https://arxiv.org/abs/2505.08142 · HTML: https://mlsanity.com/paper/2505.08142/

## 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 30 of its 70 references that are in the map.
- First posted on arXiv 13 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [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)
- [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)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformer](https://mlsanity.com/paper/2201.09376/) (2022)
- [High-Frequency Space Diffusion Models for Accelerated MRI](https://mlsanity.com/paper/2208.05481/) (2022)
- [Self-Supervised MRI Reconstruction with Unrolled Diffusion Models](https://mlsanity.com/paper/2306.16654/) (2023)
- [Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction](https://mlsanity.com/paper/2309.00783/) (2023)
- [SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI](https://mlsanity.com/paper/2304.05060/) (2023)
- [Accelerating Quantitative Susceptibility Mapping using Compressed Sensing and Deep Neural Network](https://mlsanity.com/paper/2103.09375/) (2021)
- [Fast Controllable Diffusion Models for Undersampled MRI Reconstruction](https://mlsanity.com/paper/2311.12078/) (2023)
- [Distortion-Corrected Image Reconstruction with Deep Learning on an MRI-Linac](https://mlsanity.com/paper/2205.10993/) (2022)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Score-based Diffusion Models With Self-supervised Learning For Accelerated 3D Multi-contrast Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2310.04669/) (2023)
- [Plug-and-Play Latent Feature Editing for Orientation-Adaptive Quantitative Susceptibility Mapping Neural Networks](https://mlsanity.com/paper/2311.07823/) (2023)
- [General Phase Regularized Reconstruction using Phase Cycling](https://mlsanity.com/paper/1709.05374/) (2017)

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

- [Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data](https://mlsanity.com/paper/2510.06335/) (2025)
- [Evaluating the Safety of Deep Learning-Based Brain MRI Reconstruction](https://mlsanity.com/paper/2608.28714/) (2026)

## Abstract (arXiv)

Incoherent k-space undersampling and deep learning-based reconstruction methods have shown great success in accelerating MRI. However, the performance of most previous methods will degrade dramatically under high acceleration factors, e.g., 8× or higher. Recently, denoising diffusion models (DM) have demonstrated promising results in solving this issue; however, one major drawback of the DM methods is the long inference time due to a dramatic number of iterative reverse posterior sampling steps. In this work, a Single Step Diffusion Model-based reconstruction framework, namely SSDM-MRI, is proposed for restoring MRI images from highly undersampled k-space. The proposed method achieves one-step reconstruction by first training a conditional DM and then iteratively distilling this model four times using an iterative selective distillation algorithm, which works synergistically with a shortcut reverse sampling strategy for model inference. Comprehensive experiments were carried out on both publicly available fastMRI brain and knee images, as well as an in-house multi-echo GRE (QSM) subject. Overall, the results showed that SSDM-MRI outperformed other methods in terms of numerical metrics (e.g., PSNR and SSIM), error maps, image fine details, and latent susceptibility information hidden in MRI phase images. In addition, the reconstruction time for a 320×320 brain slice of SSDM-MRI is only 0.45 second, which is only comparable to that of a simple U-net, making it a highly effective solution for MRI reconstruction tasks.