I²SB: Image-to-Image Schrödinger Bridge

Abstract

We propose Image-to-Image Schrödinger Bridge (I²SB), 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. I²SB belongs to a tractable class of Schrödinger 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 I²SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I²SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I²SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I²SB 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/