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Multi-Label Image Classification (MLIC) approaches usually exploit label correlations to achieve good performance. However, emphasizing correlation like co-occurrence may overlook discriminative features of the target itself and lead to model overfitting, thus undermining the performance. In this study, we propose a generic framework named Parallel Self-Distillation (PSD) for boosting MLIC models. PSD decomposes the original MLIC task into several simpler MLIC sub-tasks via two elaborated complementary task decomposition strategies named Co-occurrence Graph Partition (CGP) and Dis-occurrence Graph Partition (DGP). Then, the MLIC models of fewer categories are trained with these sub-tasks in parallel for respectively learning the joint patterns and the category-specific patterns of labels. Finally, knowledge distillation is leveraged to learn a compact global ensemble of full categories with these learned patterns for reconciling the label correlation exploitation and model overfitting. Extensive results on MS-COCO and NUS-WIDE datasets demonstrate that our framework can be easily plugged into many MLIC approaches and improve performances of recent state-of-the-art approaches. The explainable visual study also further validates that our method is able to learn both the category-specific and co-occurring features. The source code is released at https://github.com/Robbie-Xu/CPSD.