  Approximating distributions over complicated manifolds, such as natural
images, are conceptually attractive. The deep latent variable model, trained
using variational autoencoders and generative adversarial networks, is now a
key technique for representation learning. However, it is difficult to unify
these two models for exact latent-variable inference and parallelize both
reconstruction and sampling, partly due to the regularization under the latent
variables, to match a simple explicit prior distribution. These approaches are
prone to be oversimplified, and can only characterize a few modes of the true
distribution. Based on the recently proposed Wasserstein autoencoder (WAE) with
a new regularization as an optimal transport. The paper proposes a stacked
Wasserstein autoencoder (SWAE) to learn a deep latent variable model. SWAE is a
hierarchical model, which relaxes the optimal transport constraints at two
stages. At the first stage, the SWAE flexibly learns a representation
distribution, i.e., the encoded prior; and at the second stage, the encoded
representation distribution is approximated with a latent variable model under
the regularization encouraging the latent distribution to match the explicit
prior. This model allows us to generate natural textual outputs as well as
perform manipulations in the latent space to induce changes in the output
space. Both quantitative and qualitative results demonstrate the superior
performance of SWAE compared with the state-of-the-art approaches in terms of
faithful reconstruction and generation quality.
