Implicit Image-to-Image Schrödinger Bridge for Image Restoration

Diffusion-based models have demonstrated remarkable effectiveness in image restoration tasks; however, their iterative denoising process, which starts from Gaussian noise, often leads to slow inference speeds. The Image-to-Image Schrödinger Bridge (I²SB) offers a promising alternative by initializing the generative process from corrupted images while leveraging training techniques from score-based diffusion models. In this paper, we introduce the Implicit Image-to-Image Schrödinger Bridge (I³SB) to further accelerate the generative process of I²SB. I³SB restructures the generative process into a non-Markovian framework by incorporating the initial corrupted image at each generative step, effectively preserving and utilizing its information. To enable direct use of pretrained I²SB models without additional training, we ensure consistency in marginal distributions. Extensive experiments across many image corruptions-including noise, low resolution, JPEG compression, and sparse sampling-and multiple image modalities-such as natural, human face, and medical images- demonstrate the acceleration benefits of I³SB. Compared to I²SB, I³SB achieves the same perceptual quality with fewer generative steps, while maintaining or improving fidelity to the ground truth.