  Optimal transport (OT) provides powerful tools for comparing probability
measures in various types. The Wasserstein distance which arises naturally from
the idea of OT is widely used in many machine learning applications.
Unfortunately, computing the Wasserstein distance between two continuous
probability measures always suffers from heavy computational intractability. In
this paper, we propose an innovative algorithm that iteratively evolves a
particle system to match the optimal transport plan for two given continuous
probability measures. The derivation of the algorithm is based on the
construction of the gradient flow of an Entropy Transport Problem which could
be naturally understood as a classical Wasserstein optimal transport problem
with relaxed marginal constraints. The algorithm comes with theoretical
analysis and empirical evidence.
