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 (I$^2$SB) 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 (I$^3$SB) to further accelerate the generative process of I$^2$SB. I$^3$SB 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 I$^2$SB 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 I$^3$SB. Compared to I$^2$SB, I$^3$SB achieves the same perceptual quality with fewer generative steps, while maintaining or improving fidelity to the ground truth.

27 pages, 8 figures, accepted by Pattern Recognition