  Any autoencoder network can be turned into a generative model by imposing an
arbitrary prior distribution on its hidden code vector. Variational Autoencoder
(VAE) [2] uses a KL divergence penalty to impose the prior, whereas Adversarial
Autoencoder (AAE) [1] uses {\it generative adversarial networks} GAN [3]. GAN
trades the complexities of {\it sampling} algorithms with the complexities of
{\it searching} Nash equilibrium in minimax games. Such minimax architectures
get trained with the help of data examples and gradients flowing through a
generator and an adversary. A straightforward modification of AAE is to replace
the adversary with the maximum mean discrepancy (MMD) test [4-5]. This
replacement leads to a new type of probabilistic autoencoder, which is also
discussed in our paper. We propose a novel probabilistic autoencoder in which
the adversary of AAE is replaced with a space of {\it stochastic} functions.
This replacement introduces a new source of randomness, which can be considered
as a continuous control for encouraging {\it explorations}. This prevents the
adversary from fitting too closely to the generator and therefore leads to a
more diverse set of generated samples.
