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Although centralized training with centralized execution (CTCE) excels at multi-agent coordination, its reliance on global information limits its use in the real world. Conversely, the practical decentralized execution (CTDE) paradigm often struggles with complex coordination. This paper bridges this critical gap by introducing the Centralized-to-Decentralized (CtoD) learning concept: a novel framework for transferring the knowledge of a powerful centralized policy into a robust, practical decentralized policy. Our method, CtoD-MAT, realizes this transition through a curriculum that gradually shifts agents from centralized to decentralized control. A key innovation is our dynamic scheduling mechanism, featuring a mediator module, which ensures a robust and effective knowledge transfer. Using challenging SMAC benchmarks, we demonstrate that CtoD-MAT successfully produces competitive decentralized policies, notably solving complex coordination tasks that are difficult for standard CTDE methods.