Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions
  By building up on the recent theory that established the connection between
implicit generative modeling and optimal transport, in this study, we propose a
novel parameter-free algorithm for learning the underlying distributions of
complicated datasets and sampling from them. The proposed algorithm is based on
a functional optimization problem, which aims at finding a measure that is
close to the data distribution as much as possible and also expressive enough
for generative modeling purposes. We formulate the problem as a gradient flow
in the space of probability measures. The connections between gradient flows
and stochastic differential equations let us develop a computationally
efficient algorithm for solving the optimization problem, where the resulting
algorithm resembles the recent dynamics-based Markov Chain Monte Carlo
algorithms. We provide formal theoretical analysis where we prove finite-time
error guarantees for the proposed algorithm. Our experimental results support
our theory and shows that our algorithm is able to capture the structure of
challenging distributions.
