Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models

Diffusion bridge models have shown great promise in image restoration by explicitly connecting clean and degraded image distributions. However, they often rely on complex and high-cost trajectories, which limit both sampling efficiency and final restoration quality. To address this, we propose an Energy-oriented diffusion Bridge (E-Bridge) framework to approximate a set of low-cost manifold geodesic trajectories to boost the performance of the proposed method. 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 energy. 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 trajectory to the target image. Notably, the trajectory 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 our E-Bridge achieves state-of-the-art performance across various image restoration tasks while enabling high-quality recovery with a single or fewer sampling steps.

(a) Standard Diffusion Models: These traverse a long, high-energy trajectory starting from pure Gaussian noise to the clean image manifold, conditioned on the degraded image, they generate all information from scratch. (b) Conventional Bridge Models: These construct a path from the degraded to the clean image but often follow a sub-optimal, high-energy trajectory that includes a redundant "re-noising" phase before denoising. (c) Ours E-Bridge: It starts the reverse process from an entropy-regularized point, which is a mixture of the degraded image and noise, thus bypassing the inefficient re-noising phase and creating a more direct and shorter path for restoration.