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We consider the problem of diversifying automated reply suggestions for a commercial instant-messaging (IM) system (Skype). Our conversation model is a standard matching based information retrieval architecture, which consists of two parallel encoders to project messages and replies into a common feature representation. During inference, we select replies from a fixed response set using nearest neighbors in the feature space. To diversify responses, we formulate the model as a generative latent variable model with Conditional Variational Auto-Encoder (M-CVAE). We propose a constrained-sampling approach to make the variational inference in M-CVAE efficient for our production system. In offline experiments, M-CVAE consistently increased diversity by ∼30−40% without significant impact on relevance. This translated to a ∼5% gain in click-rate in our online production system.