The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Progressively applying Gaussian noise transforms complex data distributions to
approximately Gaussian. Reversing this dynamic defines a generative model. When the …

Solving transport problems, ie finding a map transporting one given distribution to another,
has numerous applications in machine learning. Novel mass transport methods motivated …

Simulation-free methods for training continuous-time generative models construct probability
paths that go between noise distributions and individual data samples. Recent works, such …

We analyze a number of natural estimators for the optimal transport map between two
distributions and show that they are minimax optimal. We adopt the plugin approach: our …

We consider the problem of estimating the optimal transport map between two probability
distributions, $ P $ and $ Q $ in $\mathbb {R}^ d $, on the basis of iid samples. All existing …

Flow-based models are powerful tools for designing probabilistic models with tractable
density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient …

We develop an iterative (greedy) deep learning (DL) algorithm which is able to transform an
arbitrary probability distribution function (PDF) into the target PDF. The model is based on …

We consider the problem of estimating the optimal transport map between a (fixed) source
distribution $ P $ and an unknown target distribution $ Q $, based on samples from $ Q …

We investigate the optimal transport problem between probability measures when the
underlying cost function is understood to satisfy a least action principle, also known as a …