Thanks to the reparameterization trick, deep latent Gaussian models have\nshown tremendous success recently in learning latent representations. The\nability to couple them however with nonparamet-ric priors such as the Dirichlet\nProcess (DP) hasn't seen similar success due to its non parameteriz-able\nnature. In this paper, we present an alternative treatment of the variational\nposterior of the Dirichlet Process Deep Latent Gaussian Mixture Model\n(DP-DLGMM), where we show that the prior cluster parameters and the variational\nposteriors of the beta distributions and cluster hidden variables can be\nupdated in closed-form. This leads to a standard reparameterization trick on\nthe Gaussian latent variables knowing the cluster assignments. We demonstrate\nour approach on standard benchmark datasets, we show that our model is capable\nof generating realistic samples for each cluster obtained, and manifests\ncompetitive performance in a semi-supervised setting.\n