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大多仅处理二维图像，即便是近期发布的三维方法也未能充分利用三维分布先验。为解决这一问题，我们提出一种创新方法，通过结合两个垂直预训练的二维扩散模型来求解三维逆问题。通过将三维数据分布建模为不同方向切片的二维分布乘积，该方法有效克服了维度灾难的挑战。实验结果表明，该方法在三维医学图像重建任务中表现优异，涵盖磁共振Z轴超分辨率、压缩感知磁共振及稀疏视角CT等场景。本方法可生成高质量体素体积，适用于医学应用场景。