Variational Auto-encoders (VAEs) are deep generative latent variable models\nthat are widely used for a number of downstream tasks. While it has been\ndemonstrated that VAE training can suffer from a number of pathologies,\nexisting literature lacks characterizations of exactly when these pathologies\noccur and how they impact downstream task performance. In this paper, we\nconcretely characterize conditions under which VAE training exhibits\npathologies and connect these failure modes to undesirable effects on specific\ndownstream tasks, such as learning compressed and disentangled representations,\nadversarial robustness, and semi-supervised learning.\n