Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …

This is an expository paper on the theory of gradient flows, and in particular of those PDEs
which can be interpreted as gradient flows for the Wasserstein metric on the space of …

Normalizing flows are exact-likelihood generative neural networks which approximately
transform samples from a simple prior distribution to samples of the probability distribution of …

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training
continuous normalizing flows on manifolds. Existing methods for generative modeling on …

Why a new book on optimal transport? Were the two books by Fields Medalist Cédric Villani
not enough? And what about the Bible of Gradient Flows, the book by Luigi Ambrosio …

This textbook originated from the teaching experience of the first author at the Scuola
Normale Superiore, where a course on optimal transport and its applications has been given …

This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

This text is an expanded version of the lectures given by the first author in the 2009 CIME
summer school of Cetraro. It provides a quick and reasonably account of the classical theory …

A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …