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

翻译：近年来，将可学习模块与数值优化相结合以解决低层视觉任务的方法日益受到关注。然而，现有方法大多专注于设计特定方案实现图像/特征传播，缺乏统一框架来构建传播模块、提供理论分析工具并设计有效学习机制。针对上述问题，本文提出统一优化启发式学习框架，融合生成式、判别式与校正式（简称GDC）原则，以对多种优化模型实现强泛化能力。具体而言，通过引入通用能量最小化模型并从不同视角（即生成式方式、基于判别式度量与最优性校正）构建其下降方向，我们设计了三种可灵活组合的传播模块，有效求解优化模型。进一步提出两种控制机制，为完全定义与部分定义的优化形式提供非平凡的理论保证。基于理论保证的支持，可引入归一化、搜索等多种架构增强策略，确保传播过程的收敛稳定性，并将适配模块无缝集成至传播流程中。在多种低层视觉任务上的大量实验验证了GDC的有效性与适应性。代码已开源至https://github.com/LiuZhu-CV/GDC-OptimizationLearning。