Learning Efficient and Effective Trajectories for Differential Equation-based Image Restoration

The differential equation-based image restoration approach aims to establish learnable trajectories connecting high-quality images to a tractable distribution, e.g., low-quality images or a Gaussian distribution. In this paper, we reformulate the trajectory optimization of this kind of method, focusing on enhancing both reconstruction quality and efficiency. Initially, we navigate effective restoration paths through a reinforcement learning process, gradually steering potential trajectories toward the most precise options. Additionally, to mitigate the considerable computational burden associated with iterative sampling, we propose cost-aware trajectory distillation to streamline complex paths into several manageable steps with adaptable sizes. Moreover, we fine-tune a foundational diffusion model (FLUX) with 12B parameters by using our algorithms, producing a unified framework for handling 7 kinds of image restoration tasks. Extensive experiments showcase the $\textit{significant}$ superiority of the proposed method, achieving a maximum PSNR improvement of 2.1 dB over state-of-the-art methods, while also greatly enhancing visual perceptual quality. Project page: https://zhu-zhiyu.github.io/FLUX-IR/.