# Fast Controllable Diffusion Models for Undersampled MRI Reconstruction

arXiv: https://arxiv.org/abs/2311.12078 · HTML: https://mlsanity.com/paper/2311.12078/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [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)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks](https://mlsanity.com/paper/1804.00432/) (2018)
- [Self-Supervised MRI Reconstruction with Unrolled Diffusion Models](https://mlsanity.com/paper/2306.16654/) (2023)
- [Accelerating Quantitative Susceptibility Mapping using Compressed Sensing and Deep Neural Network](https://mlsanity.com/paper/2103.09375/) (2021)

## Built on by (most cited first, 8 of 8)

- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2505.08142/) (2025)
- [Guided MRI Reconstruction via Schr"odinger Bridge](https://mlsanity.com/paper/2411.14269/) (2024)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [PWD: Prior-Guided and Wavelet-Enhanced Diffusion Model for Limited-Angle CT](https://mlsanity.com/paper/2507.05317/) (2025)
- [Real-time cardiac cine MRI -- A comparison of a diffusion probabilistic model with alternative state-of-the-art image reconstruction techniques for undersampled spiral acquisitions](https://mlsanity.com/paper/2410.04843/) (2024)
- [LDPM: Towards undersampled MRI reconstruction with MR-VAE and Latent Diffusion Prior](https://mlsanity.com/paper/2411.02951/) (2024)

## Abstract (arXiv)

Supervised deep learning methods have shown promise in undersampled Magnetic Resonance Imaging (MRI) reconstruction, but their requirement for paired data limits their generalizability to the diverse MRI acquisition parameters. Recently, unsupervised controllable generative diffusion models have been applied to undersampled MRI reconstruction, without paired data or model retraining for different MRI acquisitions. However, diffusion models are generally slow in sampling and state-of-the-art acceleration techniques can lead to sub-optimal results when directly applied to the controllable generation process. This study introduces a new algorithm called Predictor-Projector-Noisor (PPN), which enhances and accelerates controllable generation of diffusion models for undersampled MRI reconstruction. Our results demonstrate that PPN produces high-fidelity MR images that conform to undersampled k-space measurements with significantly shorter reconstruction time than other controllable sampling methods. In addition, the unsupervised PPN accelerated diffusion models are adaptable to different MRI acquisition parameters, making them more practical for clinical use than supervised learning techniques.