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:我们建议使用图像到图像Schr\'odinger Bridge(I$2$SB),这是一套新的有条件的传播模型,直接学习两种给定分布之间的非线性扩散过程。这些传播桥梁对于图像的恢复特别有用,因为退化的图像是结构信息化前重建清洁图像。 I$2$SB属于一个可移植的Schr\'odinger桥类,即分数模型的非线性扩展,其边际分布可以用分析方式计算出对边界配对。这导致一个非线性扩散的模拟无线性框架,使I$2$SB培训通过采用标准传播模型中使用的实用技术变得可升级。我们验证了I$2,SB在解决各种图像恢复任务时,包括油漆、超级分辨率、分解和JPEG在图像网络256x256上的恢复,表明I$2,SB的边际分布超过标准的有条件传播模型,并采用更易解的分解程序。此外,I$2$SB, 匹配了反向上方法的绩效,需要更多扩散模型的知识。