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.

本研究针对MRI重建中扩散模型方法面临的收敛速度慢的问题，提出了一种新颖的子空间扩散模型（Sub-DM），通过正交分解策略提升k空间数据的学习效率和图像重建质量。实验结果表明，Sub-DM在重建速度和质量方面显著优于现有先进方法，具有较大的应用潜力。

Sub-DM：具有正交分解的子空间扩散模型用于MRI重建