Consistency Geodesic Bridge: Image Restoration with Pretrained Diffusion Models

Bridge diffusion models have shown great promise in image restoration by constructing a direct path from degraded to clean images. However, they often rely on predefined, high-action trajectories, which limits both sampling efficiency and final restoration quality. To address this, we propose a Consistency Geodesic Bridge (CGB) framework to construct a lower-action, geodesic trajectory. We achieve this by designing a novel bridge process that evolves over a shorter time horizon and makes the reverse process start from an entropy-regularized point that mixes the degraded image and Gaussian noise, which theoretically reduces the required trajectory action. To ensure this path approximates a geodesic on the data manifold, we innovatively leverage a pretrained denoiser as a dynamic geodesic guidance field. To solve this process efficiently, we draw inspiration from consistency models to learn a single-step mapping function, optimized via a continuous-time consistency objective tailored for our trajectory, so as to analytically map any state on the path to the target image. Notably, the path length in our framework becomes a tunable task-adaptive knob, allowing the model to adaptively balance information preservation against generative power for tasks of varying degradation, such as denoising versus super-resolution. Extensive experiments demonstrate that CGB achieves state-of-the-art performance across various image restoration tasks, while enabling high-quality recovery with a single or fewer sampling steps. Our project page is \url{https://cgbridge.github.io/}.