# High-Frequency Space Diffusion Models for Accelerated MRI

arXiv: https://arxiv.org/abs/2208.05481 · HTML: https://mlsanity.com/paper/2208.05481/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 26 of its 66 references that are in the map.
- First posted on arXiv 10 Aug 2022.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (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)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [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)
- [Diffusion Deformable Model for 4D Temporal Medical Image Generation](https://mlsanity.com/paper/2206.13295/) (2022)
- [On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators](https://mlsanity.com/paper/1610.06665/) (2016)
- [Unpaired Deep Learning for Accelerated MRI using Optimal Transport Driven CycleGAN](https://mlsanity.com/paper/2008.12967/) (2020)
- [Data Harmonisation for Information Fusion in Digital Healthcare: A State-of-the-Art Systematic Review, Meta-Analysis and Future Research Directions](https://mlsanity.com/paper/2201.06505/) (2022)
- [Deep Manifold Learning for Dynamic MR Imaging](https://mlsanity.com/paper/2104.01102/) (2021)
- [Self-supervised Deep Unrolled Reconstruction Using Regularization by Denoising](https://mlsanity.com/paper/2205.03519/) (2022)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)
- [On-the-fly Adaptive k-Space Sampling for Linear MRI Reconstruction Using Moment-Based Spectral Analysis](https://mlsanity.com/paper/1710.07837/) (2017)
- [Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space](https://mlsanity.com/paper/1310.7489/) (2013)

## Built on by (most cited first, 30 of 42)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [3D MedDiffusion: A 3D Medical Latent Diffusion Model for Controllable and High-quality Medical Image Generation](https://mlsanity.com/paper/2412.13059/) (2024)
- [Fast-DDPM: Fast Denoising Diffusion Probabilistic Models for Medical Image-to-Image Generation](https://mlsanity.com/paper/2405.14802/) (2024)
- [Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis](https://mlsanity.com/paper/2410.02321/) (2024)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI](https://mlsanity.com/paper/2304.05060/) (2023)
- [Self-Supervised Adversarial Diffusion Models for Fast MRI Reconstruction](https://mlsanity.com/paper/2406.15656/) (2024)
- [FairGen: Controlling Sensitive Attributes for Fair Generations in Diffusion Models via Adaptive Latent Guidance](https://mlsanity.com/paper/2503.01872/) (2025)
- [MRI Super-Resolution with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2511.16854/) (2025)
- [Diffusion Model Quantization: A Review](https://mlsanity.com/paper/2505.05215/) (2025)
- [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)
- [MRPD: Undersampled MRI reconstruction by prompting a large latent diffusion model](https://mlsanity.com/paper/2402.10609/) (2024)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Exploring the latent space of diffusion models directly through singular value decomposition](https://mlsanity.com/paper/2502.02225/) (2025)
- [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)
- [Diff-DTI: Fast Diffusion Tensor Imaging Using A Feature-Enhanced Joint Diffusion Model](https://mlsanity.com/paper/2405.15830/) (2024)
- [Robust Simultaneous Multislice MRI Reconstruction Using Slice-Wise Learned Generative Diffusion Priors](https://mlsanity.com/paper/2407.21600/) (2024)
- [Diff-INR: Generative Regularization for Electrical Impedance Tomography](https://mlsanity.com/paper/2409.04494/) (2024)
- [Highly Undersampled MRI Reconstruction via a Single Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2505.08142/) (2025)
- [Accelerating MRI with Longitudinally-informed Latent Posterior Sampling](https://mlsanity.com/paper/2407.00537/) (2024)
- [Self-Consistent Nested Diffusion Bridge for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2412.09998/) (2024)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Exploring the Power of Generative Deep Learning for Image-to-Image Translation and MRI Reconstruction: A Cross-Domain Review](https://mlsanity.com/paper/2303.09012/) (2023)
- [The object detection method aids in image reconstruction evaluation and clinical interpretation of meniscal abnormalities](https://mlsanity.com/paper/2407.12184/) (2024)
- [TC-KANRecon: High-Quality and Accelerated MRI Reconstruction via Adaptive KAN Mechanisms and Intelligent Feature Scaling](https://mlsanity.com/paper/2408.05705/) (2024)

## Abstract (arXiv)

Diffusion models with continuous stochastic differential equations (SDEs) have shown superior performances in image generation. It can serve as a deep generative prior to solving the inverse problem in magnetic resonance (MR) reconstruction. However, low-frequency regions of k-space data are typically fully sampled in fast MR imaging, while existing diffusion models are performed throughout the entire image or k-space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. Additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. To address these challenges, we propose a novel SDE tailored specifically for MR reconstruction with the diffusion process in high-frequency space (referred to as HFS-SDE). This approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. Experiments conducted on the publicly available fastMRI dataset demonstrate that the proposed HFS-SDE method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. The fast convergence properties are also confirmed through theoretical and experimental validation. Our code and weights are available at https://github.com/Aboriginer/HFS-SDE.