arXiv:2606. 30053v1 Announce Type: cross Abstract: These notes recapitulate the high level mathematical principles behind different techniques for generative modeling.
By Titouan Vayer (COMPACT)
arXiv:2605.29713v2 Announce Type: replace-cross
Abstract: This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence....
By Tianhua Chen
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
By Sivaraman Balakrishnan
arXiv:2509.26364v3 Announce Type: replace
Abstract: The Schr\"odinger bridge problem is concerned with finding a stochastic dynamical system bridging two marginal distributions that minimises a certa...
By Kirill Tamogashev, Esmeralda S. Whitammer
arXiv:2609.15072v1 Announce Type: cross
Abstract: Methods of Branched Optimal Transport (BOT) mimic the economy and efficiency of natural tree-like structures, such as those found in rivers and biolo...
By Semyon Semenov, Viktor Kovalchuk, Meir Roketlishvili, Albert Baichorov, Fakhri Karray, Martin Takac, Arip Asadulaev