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 and codes: https://i2sb.github.io/

翻译：我们提出图像到图像薛定谔桥（I$^2$SB），这是一类新的条件扩散模型，能够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特别有用，因为退化图像是重建清晰图像的结构性先验信息。I$^2$SB属于一类可解的薛定谔桥——基于分数的模型的非线性扩展，其边界分布对之间的边际分布可以解析计算。这使得非线性扩散无需模拟即可训练，通过采用标准扩散模型中的实用技术，I$^2$SB的训练可以规模化。我们在解决各种图像复原任务中验证了I$^2$SB，包括ImageNet 256x256上的图像修复、超分辨率、去模糊和JPEG复原，结果表明I$^2$SB以更可解释的生成过程超越了标准条件扩散模型。此外，I$^2$SB的性能与额外需要退化算子知识的逆方法相当。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会。项目页面和代码：https://i2sb.github.io/