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Heterogeneous information network (HIN) embedding, aiming to map the structure and semantic information in a HIN to distributed representations, has drawn considerable research attention. Graph neural networks for HIN embeddings typically adopt a hierarchical attention (including node-level and meta-path-level attentions) to capture the information from meta-path-based neighbors. However, this complicated attention structure often cannot achieve the function of selecting meta-paths due to severe overfitting. Moreover, when propagating information, these methods do not distinguish direct (one-hop) meta-paths from indirect (multi-hop) ones. But from the perspective of network science, direct relationships are often believed to be more essential, which can only be used to model direct information propagation. To address these limitations, we propose a novel neural network method via implicitly utilizing attention and meta-paths, which can relieve the severe overfitting brought by the current over-parameterized attention mechanisms on HIN. We first use the multi-layer graph convolutional network (GCN) framework, which performs a discriminative aggregation at each layer, along with stacking the information propagation of direct linked meta-paths layer-by-layer, realizing the function of attentions for selecting meta-paths in an indirect way. We then give an effective relaxation and improvement via introducing a new propagation operation which can be separated from aggregation. That is, we first model the whole propagation process with well-defined probabilistic diffusion dynamics, and then introduce a random graph-based constraint which allows it to reduce noise with the increase of layers. Extensive experiments demonstrate the superiority of the new approach over state-of-the-art methods.