Image-to-image translation is defined as the process of learning a mapping between images from a source domain and images from a target domain. The probabilistic structure that maps a fixed initial state to a pinned terminal state through a standard Wiener process is a Brownian bridge. In this paper, we propose a score-based Stochastic Differential Equation (SDE) approach via the Brownian bridges, termed the Amenable Brownian Bridges (A-Bridges), to image-to-image translation tasks as an unconditional diffusion model. Our framework embraces a large family of Brownian bridge models, while the discretization of the linear A-Bridge exploits its advantage that provides the explicit solution in a closed form and thus facilitates the model training. Our model enables the accelerated sampling and has achieved record-breaking performance in sample quality and diversity on benchmark datasets following the guidance of its SDE structure.
Keywords: A-Bridges; Brownian Bridge; Diffusion Models; Generative Models; Image-to-Image Translation; Score-Based Models; Stochastic Differential Equations (SDE); Unconditional Diffusion Process.