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To the same utterance, people's responses in everyday dialogue may be diverse largely in terms of content semantics, speaking styles, communication intentions and so on. Previous generative conversational models ignore these 1-to-n relationships between a post to its diverse responses, and tend to return high-frequency but meaningless responses. In this study we propose a mechanism-aware neural machine for dialogue response generation. It assumes that there exists some latent responding mechanisms, each of which can generate different responses for a single input post. With this assumption we model different responding mechanisms as latent embeddings, and develop a encoder-diverter-decoder framework to train its modules in an end-to-end fashion. With the learned latent mechanisms, for the first time these decomposed modules can be used to encode the input into mechanism-aware context, and decode the responses with the controlled generation styles and topics. Finally, the experiments with human judgements, intuitive examples, detailed discussions demonstrate the quality and diversity of the generated responses with 9.80% increase of acceptable ratio over the best of six baseline methods.