Neural Machine Translation (NMT) models often lack diversity in their generated translations, even when paired with search algorithm, like beam search. A challenge is that the diversity in translations are caused by the variability in the target language, and cannot be inferred from the source sentence alone. In this paper, we propose to explicitly model this one-to-many mapping by conditioning the decoder of a NMT model on a latent variable that represents the domain of target sentences. The domain is a discrete variable generated by a target encoder that is jointly trained with the NMT model.The predicted domain of target sentences are given as input to the decoder during training. At inference, we can generate diverse translations by decoding with different domains. Unlike our strongest baseline (Shen et al., 2019), our method can scale to any number of domains without affecting the performance or the training time. We assess the quality and diversity of translations generated by our model with several metrics, on three different datasets.