# Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction

arXiv: https://arxiv.org/abs/2309.00853 · HTML: https://mlsanity.com/paper/2309.00853/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 2 Sep 2023.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (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)
- [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)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (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)
- [Accelerating Diffusion Models via Early Stop of the Diffusion Process](https://mlsanity.com/paper/2205.12524/) (2022)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Models](https://mlsanity.com/paper/2302.03018/) (2023)
- [Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance](https://mlsanity.com/paper/2212.06359/) (2022)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Data](https://mlsanity.com/paper/2109.03812/) (2021)
- [Homotopic Gradients of Generative Density Priors for MR Image Reconstruction](https://mlsanity.com/paper/2008.06284/) (2020)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI](https://mlsanity.com/paper/2304.05060/) (2023)
- [Accelerating Score-based Generative Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2206.04029/) (2022)
- [Structure Preserving Compressive Sensing MRI Reconstruction using Generative Adversarial Networks](https://mlsanity.com/paper/1910.06067/) (2019)
- [MRI Reconstruction Using Deep Energy-Based Model](https://mlsanity.com/paper/2109.03237/) (2021)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [Geometry of Score Based Generative Models](https://mlsanity.com/paper/2302.04411/) (2023)

## Built on by (most cited first, 14 of 14)

- [Generative AI for Synthetic Data Across Multiple Medical Modalities: A Systematic Review of Recent Developments and Challenges](https://mlsanity.com/paper/2407.00116/) (2024)
- [Physics-Inspired Generative Models in Medical Imaging: A Review](https://mlsanity.com/paper/2407.10856/) (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)
- [DP-MDM: Detail-Preserving MR Reconstruction via Multiple Diffusion Models](https://mlsanity.com/paper/2405.05763/) (2024)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [A Brief Overview of Optimization-Based Algorithms for MRI Reconstruction Using Deep Learning](https://mlsanity.com/paper/2406.02626/) (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)
- [Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction](https://mlsanity.com/paper/2411.03758/) (2024)
- [A Comprehensive Survey on Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2503.07097/) (2025)
- [MS-Glance: Bio-Insipred Non-semantic Context Vectors and their Applications in Supervising Image Reconstruction](https://mlsanity.com/paper/2410.23577/) (2024)
- [Dual-domain Multi-path Self-supervised Diffusion Model for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2503.18836/) (2025)
- [Adaptive Mask-guided K-space Diffusion for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2506.18270/) (2025)
- [Diffusion-Assisted Frequency Attention Model for Whole-body Low-field MRI Reconstruction](https://mlsanity.com/paper/2507.17764/) (2025)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)

## Abstract (arXiv)

Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for diagnosis. In this study, leveraging a combination of the properties of k-space data and the diffusion process, our novel scheme focuses on mining the multi-frequency prior with different strategies to pre-serve fine texture details in the reconstructed image. In addition, a diffusion process can converge more quickly if its target distribution closely resembles the noise distri-bution in the process. This can be accomplished through various high-frequency prior extractors. The finding further solidifies the effectiveness of the score-based gen-erative model. On top of all the advantages, our method improves the accuracy of MRI reconstruction and accel-erates sampling process. Experimental results verify that the proposed method successfully obtains more accurate reconstruction and outperforms state-of-the-art methods.