Dialogue summarization aims to generate a summary that indicates the key points of a given dialogue. In this work, we propose an end-to-end neural model for dialogue summarization with two novel modules, namely, the supporting utterance flow modelling module and the fact regularization module. The supporting utterance flow modelling helps to generate a coherent summary by smoothly shifting the focus from the former utterances to the later ones. The fact regularization encourages the generated summary to be factually consistent with the ground-truth summary during model training, which helps to improve the factual correctness of the generated summary in inference time. Furthermore, we also introduce a new benchmark dataset for dialogue summarization. Extensive experiments on both existing and newly-introduced datasets demonstrate the effectiveness of our model.