  Generative AutoEncoders require a chosen probability distribution in latent
space, usually multivariate Gaussian. The original Variational AutoEncoder
(VAE) uses randomness in encoder - causing problematic distortion, and overlaps
in latent space for distinct inputs. It turned out unnecessary: we can instead
use deterministic encoder with additional regularizer to ensure that sample
distribution in latent space is close to the required. The original approach
(WAE) uses Wasserstein metric, what required comparing with random sample and
using an arbitrarily chosen kernel. Later CWAE finally derived a non-random
analytic formula by averaging $L_2$ distance of Gaussian-smoothened sample over
all 1D projections. However, these arbitrarily chosen regularizers do not lead
to Gaussian distribution.
  This article proposes approach for regularizers directly optimizing agreement
between empirical distribution function and its desired CDF for chosen
properties, for example radii and distances for Gaussian distribution, or
coordinate-wise, to directly attract this distribution in latent space of
AutoEncoder. We can also attract different distributions with this general
approach, for example latent space uniform distribution on $[0,1]^D$ hypercube
or torus would allow for data compression without entropy coding, increased
density near codewords would optimize for the required quantization.
