Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$). In the case where the codomain has known structure, a large unfeatured dataset ($\mathbf{y}$) is potentially available. We develop a parameter-efficient, deep semi-supervised generative model for the purpose of exploiting this untapped data source. Empirical results show improved performance in disentangling latent variable semantics as well as improved discriminative prediction on Martian spectroscopic and handwritten digit domains.