As an important problem in causal inference, we discuss the estimation of treatment effects (TEs). Representing the confounder as a latent variable, we propose Intact-VAE, a new variant of variational autoencoder (VAE), motivated by the prognostic score that is sufficient for identifying TEs. Our VAE also naturally gives representations balanced for treatment groups, using its prior. Experiments on (semi-)synthetic datasets show state-of-the-art performance under diverse settings, including unobserved confounding. Based on the identifiability of our model, we prove identification of TEs under unconfoundedness, and also discuss (possible) extensions to harder settings.Comment: Fully updated. Largely improve clarity, add identification under unconfoundedness (Sec. 4.2), and more. arXiv admin note: substantial text overlap with arXiv:2101.06662