  Variational Autoencoder (VAE) and its variations are classic generative
models by learning a low-dimensional latent representation to satisfy some
prior distribution (e.g., Gaussian distribution). Their advantages over GAN are
that they can simultaneously generate high dimensional data and learn latent
representations to reconstruct the inputs. However, it has been observed that a
trade-off exists between reconstruction and generation since matching prior
distribution may destroy the geometric structure of data manifold. To mitigate
this problem, we propose to let the prior match the embedding distribution
rather than imposing the latent variables to fit the prior. The embedding
distribution is trained using a simple regularized autoencoder architecture
which preserves the geometric structure to the maximum. Then an adversarial
strategy is employed to achieve a latent mapping. We provide both theoretical
and experimental support for the effectiveness of our method, which alleviates
the contradiction between topological properties' preserving of data manifold
and distribution matching in latent space.
