We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for image restoration, as the degraded images are structurally informative priors for reconstructing the clean images. I$^2$SB belongs to a tractable class of Schr\"odinger bridge, the nonlinear extension to score-based models, whose marginal distributions can be computed analytically given boundary pairs. This results in a simulation-free framework for nonlinear diffusions, where the I$^2$SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I$^2$SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I$^2$SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I$^2$SB matches the performance of inverse methods that additionally require the knowledge of the corruption operators. Our work opens up new algorithmic opportunities for developing efficient nonlinear diffusion models on a large scale. scale. Project page: https://i2sb.github.io/

翻译：我们提出图像到图像的薛定谔桥（I$^2$SB），这是一类新型条件扩散模型，可直接学习两个给定分布之间的非线性扩散过程。这些扩散桥对于图像复原尤为有效，因为退化图像是重建清晰图像的结构性信息先验。I$^2$SB属于可解薛定谔桥类别，是得分模型（score-based models）的非线性扩展，其边际分布在给定边界对时可解析计算。这实现了无模拟的非线性扩散框架，通过采用标准扩散模型中的实用技术，I$^2$SB训练变得可扩展。我们在ImageNet 256x256上验证了I$^2$SB在多种图像复原任务（包括图像修复、超分辨率、去模糊和JPEG复原）中的表现，结果表明I$^2$SB超越了标准条件扩散模型，并具有更可解释的生成过程。此外，I$^2$SB达到了需要额外知道退化算子的逆方法的性能。我们的工作为大规模开发高效非线性扩散模型开辟了新的算法机遇。项目页面：https://i2sb.github.io/