  In recent years, there has been a growing interest in combining learnable
modules with numerical optimization to solve low-level vision tasks. However,
most existing approaches focus on designing specialized schemes to generate
image/feature propagation. There is a lack of unified consideration to
construct propagative modules, provide theoretical analysis tools, and design
effective learning mechanisms. To mitigate the above issues, this paper
proposes a unified optimization-inspired learning framework to aggregate
Generative, Discriminative, and Corrective (GDC for short) principles with
strong generalization for diverse optimization models. Specifically, by
introducing a general energy minimization model and formulating its descent
direction from different viewpoints (i.e., in a generative manner, based on the
discriminative metric and with optimality-based correction), we construct three
propagative modules to effectively solve the optimization models with flexible
combinations. We design two control mechanisms that provide the non-trivial
theoretical guarantees for both fully- and partially-defined optimization
formulations. Under the support of theoretical guarantees, we can introduce
diverse architecture augmentation strategies such as normalization and search
to ensure stable propagation with convergence and seamlessly integrate the
suitable modules into the propagation respectively. Extensive experiments
across varied low-level vision tasks validate the efficacy and adaptability of
GDC. The codes are available at
https://github.com/LiuZhu-CV/GDC-OptimizationLearning
