  Variational autoencoders (VAE) often use Gaussian or category distribution to
model the inference process. This puts a limit on variational learning because
this simplified assumption does not match the true posterior distribution,
which is usually much more sophisticated. To break this limitation and apply
arbitrary parametric distribution during inference, this paper derives a
\emph{semi-continuous} latent representation, which approximates a continuous
density up to a prescribed precision, and is much easier to analyze than its
continuous counterpart because it is fundamentally discrete. We showcase the
proposition by applying polynomial exponential family distributions as the
posterior, which are universal probability density function generators. Our
experimental results show consistent improvements over commonly used VAE
models.
