# Sub-DM:Subspace Diffusion Model with Orthogonal Decomposition for MRI Reconstruction

arXiv: https://arxiv.org/abs/2411.03758 · HTML: https://mlsanity.com/paper/2411.03758/

## 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 27 of its 53 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [CoLa-Diff: Conditional Latent Diffusion Model for Multi-Modal MRI Synthesis](https://mlsanity.com/paper/2303.14081/) (2023)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [CleanDiffuser: An Easy-to-use Modularized Library for Diffusion Models in Decision Making](https://mlsanity.com/paper/2406.09509/) (2024)
- [Deep Learning with Domain Adaptation for Accelerated Projection-Reconstruction MR](https://mlsanity.com/paper/1703.01135/) (2017)
- [Rethinking Diffusion Model for Multi-Contrast MRI Super-Resolution](https://mlsanity.com/paper/2404.04785/) (2024)
- [fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Data](https://mlsanity.com/paper/2109.03812/) (2021)
- [SMRD: SURE-based Robust MRI Reconstruction with Diffusion Models](https://mlsanity.com/paper/2310.01799/) (2023)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [Dimensionality-Varying Diffusion Process](https://mlsanity.com/paper/2211.16032/) (2022)
- [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)
- [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)

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

- [Adaptive Mask-guided K-space Diffusion for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2506.18270/) (2025)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)

## Abstract (arXiv)

Diffusion model-based approaches recently achieved re-markable success in MRI reconstruction, but integration into clinical routine remains challenging due to its time-consuming convergence. This phenomenon is partic-ularly notable when directly apply conventional diffusion process to k-space data without considering the inherent properties of k-space sampling, limiting k-space learning efficiency and image reconstruction quality. To tackle these challenges, we introduce subspace diffusion model with orthogonal decomposition, a method (referred to as Sub-DM) that restrict the diffusion process via projections onto subspace as the k-space data distribution evolves toward noise. Particularly, the subspace diffusion model circumvents the inference challenges posed by the com-plex and high-dimensional characteristics of k-space data, so the highly compact subspace ensures that diffusion process requires only a few simple iterations to produce accurate prior information. Furthermore, the orthogonal decomposition strategy based on wavelet transform hin-ders the information loss during the migration of the vanilla diffusion process to the subspace. Considering the strate-gy is approximately reversible, such that the entire pro-cess can be reversed. As a result, it allows the diffusion processes in different spaces to refine models through a mutual feedback mechanism, enabling the learning of ac-curate prior even when dealing with complex k-space data. Comprehensive experiments on different datasets clearly demonstrate that the superiority of Sub-DM against state of-the-art methods in terms of reconstruction speed and quality.