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Multi-layered inter-dependent networks have emerged in a wealth of high-impact application domains. Cross-layer dependency inference, which aims to predict the dependencies between nodes across different layers, plays a pivotal role in such multi-layered network systems. Most, if not all, of existing methods exclusively follow a coupling principle of design and can be categorized into the following two groups, including (1) heterogeneous network embedding based methods (data coupling), and (2) collaborative filtering based methods (module coupling). Despite the favorable achievement, methods of both types are faced with two intricate challenges, including (1) the sparsity challenge where very limited observations of cross-layer dependencies are available, resulting in a deteriorated prediction of missing dependencies, and (2) the dynamic challenge given that the multi-layered network system is constantly evolving over time. In this paper, we first demonstrate that the inability of existing methods to resolve the sparsity challenge roots in the coupling principle from the perspectives of both data coupling and module coupling. Armed with such theoretical analysis, we pursue a new principle where the key idea is to decouple the within-layer connectivity from the observed cross-layer dependencies. Specifically, to tackle the sparsity challenge for static networks, we propose FITO-S, which incorporates a position embedding matrix generated by random walk with restart and the embedding space transformation function. More essentially, the decoupling principle ameliorates the dynamic challenge, which naturally leads to FITO-D, being capable of tracking the inference results in the dynamic setting through incrementally updating the position embedding matrix and fine-tuning the space transformation function. Extensive evaluations on real-world datasets demonstrate the superiority of the proposed framework FITO for cross-layer dependency inference.