Normalizing Flows are generative models which produce tractable distributions where both
sampling and density evaluation can be efficient and exact. The goal of this survey article is …

Optimal transport has recently been reintroduced to the machine learning community thanks
in part to novel efficient optimization procedures allowing for medium to large scale …

Optimal transport distances have found many applications in machine learning for their
capacity to compare non-parametric probability distributions. Yet their algorithmic complexity …

The Wasserstein distance and its variations, eg, the sliced-Wasserstein (SW) distance, have
recently drawn attention from the machine learning community. The SW distance …

We propose to learn a generative model via entropy interpolation with a Schr {ö} dinger
Bridge. The generative learning task can be formulated as interpolating between a reference …

In this paper we use the geometric properties of the optimal transport (OT) problem and the
Wasserstein distances to define a prior distribution for the latent space of an auto-encoder …

Optimal transport (OT) methods seek a transformation map (or plan) between two probability
measures, such that the transformation has the minimum transportation cost. Such a …

Wasserstein gradient flows provide a powerful means of understanding and solving many
diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of …

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and
study its convergence properties. The MMD is an integral probability metric defined for a …

Optimal transport (OT) has become exceedingly popular in machine learning, data science,
and computer vision. The core assumption in the OT problem is the equal total amount of …