Abstract: RGB cloth generation has been deeply studied in the related literature, however, 3D garment generation remains an open problem. In this paper, we build a conditional variational autoencoder for 3D garment generation and draping. We propose a pyramid network to add garment details progressively in a canonical space, i.e. unposing and unshaping the garments w.r.t. the body. We study conditioning the network on surface normal UV maps, as an intermediate representation, which is an easier problem to optimize than 3D coordinates. Our results on two public datasets, CLOTH3D and CAPE, show that our model is robust, controllable in terms of detail generation by the use of multi-resolution pyramids, and achieves state-of-the-art results that can highly generalize to unseen garments, poses, and shapes even when training with small amounts of data.