In human conversation an input post is open to multiple potential responses, which is typically regarded as a one-to-many problem. Promising approaches mainly incorporate multiple latent mechanisms to build the one-to-many relationship. However, without accurate selection of the latent mechanism corresponding to the target response during training, these methods suffer from a rough optimization of latent mechanisms. In this paper, we propose a multi-mapping mechanism to better capture the one-to-many relationship, where multiple mapping modules are employed as latent mechanisms to model the semantic mappings from an input post to its diverse responses. For accurate optimization of latent mechanisms, a posterior mapping selection module is designed to select the corresponding mapping module according to the target response for further optimization. We also introduce an auxiliary matching loss to facilitate the optimization of posterior mapping selection. Empirical results demonstrate the superiority of our model in generating multiple diverse and informative responses over the state-of-the-art methods.