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In the last decade, information diffusion (also known as information cascade) on social networks has been massively investigated due to its application values in many fields. In recent years, many sequential models including those models based on recurrent neural networks have been broadly employed to predict information cascade. However, the user dependencies in a cascade sequence captured by sequential models are generally unidirectional and inconsistent with diffusion trees. For example, the true trigger of a successor may be a non-immediate predecessor rather than the immediate predecessor in the sequence. To capture user dependencies more sufficiently which are crucial to precise cascade modeling, we propose a non-sequential information cascade model named as TAN-DRUD (Topology-aware Attention Networks with Dual Role User Dependency). TAN-DRUD obtains satisfactory performance on information cascade modeling through capturing the dual role user dependencies of information sender and receiver, which is inspired by the classic communication theory. Furthermore, TANDRUD incorporates social topology into two-level attention networks for enhanced information diffusion prediction. Our extensive experiments on three cascade datasets demonstrate that our model is not only superior to the state-of-the-art cascade models, but also capable of exploiting topology information and inferring diffusion trees.