Deep neural networks (DNNs) for generative mixture modeling typically rely on unsupervised learning that employs hard clustering schemes, or variational learning with loose / approximate bounds, or under-regularized modeling. We propose a novel statistical framework for a DNN mixture model using a single generative adversarial network. Our learning formulation proposes a novel data-likelihood term relying on a well-regularized / constrained Gaussian mixture model in the latent space along with a prior term on the DNN weights. Our min-max learning increases the data likelihood using a tight variational lower bound using expectation maximization (EM). We leverage our min-max EM learning scheme for semi-supervised learning. Results on three real-world datasets demonstrate the benefits of our compact modeling and learning formulation over the state of the art for mixture modeling and clustering.