In this paper, we delve deeper into the Kullback-Leibler (KL) Divergence loss and mathematically prove that it is equivalent to the Decoupled Kullback-Leibler (DKL) Divergence loss that consists of (1) a weighted Mean Square Error (wMSE) loss and (2) a Cross-Entropy loss incorporating soft labels. Thanks to the decoupled structure of DKL loss, we have identified two areas for improvement. Firstly, we address the limitation of KL loss in scenarios like knowledge distillation by breaking its asymmetric optimization property along with a smoother weight function. This modification effectively alleviates convergence challenges in optimization, particularly for classes with high predicted scores in soft labels. Secondly, we introduce class-wise global information into KL/DKL to reduce bias arising from individual samples. With these two enhancements, we derive the Generalized Kullback-Leibler (GKL) Divergence loss and evaluate its effectiveness by conducting experiments on CIFAR-10/100, ImageNet, and vision-language datasets, focusing on adversarial training, and knowledge distillation tasks. Specifically, we achieve new state-of-the-art adversarial robustness on the public leaderboard -- RobustBench and competitive knowledge distillation performance across CIFAR/ImageNet models and CLIP models, demonstrating the substantial practical merits. Our code is available at https://github.com/jiequancui/DKL.

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