  The Gaussianity assumption has been consistently criticized as a main
limitation of the Variational Autoencoder (VAE) despite its efficiency in
computational modeling. In this paper, we propose a new approach that expands
the model capacity (i.e., expressive power of distributional family) without
sacrificing the computational advantages of the VAE framework. Our VAE model's
decoder is composed of an infinite mixture of asymmetric Laplace distribution,
which possesses general distribution fitting capabilities for continuous
variables. Our model is represented by a special form of a nonparametric
M-estimator for estimating general quantile functions, and we theoretically
establish the relevance between the proposed model and quantile estimation. We
apply the proposed model to synthetic data generation, and particularly, our
model demonstrates superiority in easily adjusting the level of data privacy.
