Project, Skate, and Refresh: Improved Schrödinger Bridge Sampler for Image Restoration

The recent advancements in diffusion model-based image restoration (DMIR) have attracted significant attention, particularly the Image-to-Image Schrödinger Bridge ($\mathrm{I}^{2} \mathrm{SB}$) method. This approach has surpassed previous state-of-the-art (SOTA) benchmarks in handling complex data distributions, including ImageNet. However, $I^{2}$ SB faces challenges with three main estimation errors: original image estimation error at current step, next step image estimation error, and persistent random errors. These issues contribute to artifacts in the output. Our research focuses on overcoming these limitations. We introduce a set of three innovative algorithms, named PSR (Project, Skate, and Refresh), designed to efficiently address the estimation errors in $\mathrm{I}^{2} \mathrm{SB}$ without extra training. ‘Project’ aligns the current moment’s image estimation with the original space of the image restoration problem. ‘Skate’ follows the gradient descent on the manifold to correct the next moment’s image estimation error. ‘Refresh’ diminishes random errors at any step. PSR integrates smoothly with $\mathrm{I}^{2} \mathrm{SB}$ model, showing minimal additional computational load. Our tests on ImageNet demonstrate that PSR greatly outperforms the $\mathrm{I}^{2} \mathrm{SB}$ method in tasks like deblurring, super-resolution, and JPEG artifact removal, achieving new SOTA on public benchmarks in metrics such as FID, SSIM, and PSNR.