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Value Decomposition (VD) aims to deduce the contributions of agents for decentralized policies in the presence of only global rewards, and has recently emerged as a powerful credit assignment paradigm for tackling cooperative Multi-Agent Reinforcement Learning (MARL) problems. One of the main challenges in VD is to promote diverse behaviors among agents, while existing methods directly encourage the diversity of learned agent networks with various strategies. However, we argue that these dedicated designs for agent networks are still limited by the indistinguishable VD network, leading to homogeneous agent behaviors and thus downgrading the cooperation capability. In this paper, we propose a novel Contrastive Identity-Aware learning (CIA) method, explicitly boosting the credit-level distinguishability of the VD network to break the bottleneck of multi-agent diversity. Specifically, our approach leverages contrastive learning to maximize the mutual information between the temporal credits and identity representations of different agents, encouraging the full expressiveness of credit assignment and further the emergence of individualities. The algorithm implementation of the proposed CIA module is simple yet effective that can be readily incorporated into various VD architectures. Experiments on the SMAC benchmarks and across different VD backbones demonstrate that the proposed method yields results superior to the state-of-the-art counterparts. Our code is available at https://github.com/liushunyu/CIA.