Abstract: Retrieving the proper knowledge relevant to conversational context is an important challenge in dialogue systems, to engage users with more informative response. Several recent works propose to formulate this knowledge selection problem as a path traversal over an external knowledge graph (KG), but show only a limited utilization of KG structure, leaving rooms of improvement in performance. To this effect, we present AttnIO, a new dialog-conditioned path traversal model that makes a full use of rich structural information in KG based on two directions of attention flows. Through the attention flows, AttnIO is not only capable of exploring a broad range of multi-hop knowledge paths, but also learns to flexibly adjust the varying range of plausible nodes and edges to attend depending on the dialog context. Empirical evaluations present a marked performance improvement of AttnIO compared to all baselines in OpenDialKG dataset. Also, we find that our model can be trained to generate an adequate knowledge path even when the paths are not available and only the destination nodes are given as label, making it more applicable to real-world dialogue systems.