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.

翻译：基于扩散模型的方法最近在磁共振成像重建中取得了显著成功，但由于其耗时的收敛过程，融入临床常规仍面临挑战。当直接将传统扩散过程应用于k空间数据而未考虑k空间采样的固有特性时，这种现象尤为明显，这限制了k空间的学习效率和图像重建质量。为应对这些挑战，我们引入了基于正交分解的子空间扩散模型（简称Sub-DM），该方法通过在k空间数据分布向噪声演化时，将扩散过程限制在子空间投影上进行。特别地，子空间扩散模型规避了k空间数据复杂高维特性带来的推理挑战，因此高度紧凑的子空间确保扩散过程仅需少量简单迭代即可产生准确的先验信息。此外，基于小波变换的正交分解策略抑制了原始扩散过程迁移至子空间时的信息损失。考虑到该策略近似可逆，整个过程可以反向进行。因此，它允许不同空间中的扩散过程通过相互反馈机制优化模型，即使在处理复杂k空间数据时也能学习准确的先验。在不同数据集上的综合实验清楚地证明了Sub-DM在重建速度和质量方面相较于现有先进方法的优越性。