Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

翻译：扩散模型因其众多优势，已成为图像生成与重建领域的主流方法。然而，现有基于扩散模型的逆问题求解方法主要针对二维图像，近期提出的三维方法也未能充分挖掘三维分布先验。为此，本文提出一种创新方法：通过两个正交的预训练二维扩散模型求解三维逆问题。该方法将三维数据分布建模为不同方向切片得到的二维分布之积，有效克服了维度灾难问题。实验结果表明，该方法在三维医学图像重建任务（包括MRI Z轴超分辨率、压缩感知MRI和稀疏视角CT）中展现出卓越性能，可生成适用于医学应用的高质量体素体数据。