Human conversations naturally evolve around related concepts and hop to distant concepts. This paper presents a new conversation generation model, ConceptFlow, which leverages commonsense knowledge graphs to explicitly model conversation flows. By grounding conversations to the concept space, ConceptFlow represents the potential conversation flow as traverses in the concept space along commonsense relations. The traverse is guided by graph attentions in the concept graph, moving towards more meaningful directions in the concept space, in order to generate more semantic and informative responses. Experiments on Reddit conversations demonstrate ConceptFlow’s effectiveness over previous knowledge-aware conversation models and GPT-2 based models while using 70% fewer parameters, confirming the advantage of explicit modeling conversation structures. All source codes of this work are available at https://github.com/thunlp/ConceptFlow.