  Generative modelling is a key tool in unsupervised machine learning which has
achieved stellar success in recent years. Despite this huge success, even the
best generative models such as Generative Adversarial Networks (GANs) and
Variational Autoencoders (VAEs) come with their own shortcomings, mode collapse
and mode mixture being the two most prominent problems. In this paper we
develop a new generative model capable of generating samples which resemble the
observed data, and is free from mode collapse and mode mixture. Our model is
inspired by the recently proposed Autoencoder-Optimal Transport (AE-OT) model
and tries to improve on it by addressing the problems faced by the AE-OT model
itself, specifically with respect to the sample generation algorithm.
Theoretical results concerning the bound on the error in approximating the
non-smooth Brenier potential by its smoothed estimate, and approximating the
discontinuous optimal transport map by a smoothed optimal transport map
estimate have also been established in this paper.
