These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr{ö}dinger bridge and flow matching.
arXiv:2606. 30053v1 Announce Type: cross Abstract: These notes recapitulate the high level mathematical principles behind different techniques for generative modeling.
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....
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.
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...
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...
arXiv:2606. 15897v1 Announce Type: cross Abstract: Flow matching is a powerful generative modeling framework, valued for its simplicity and strong empirical performance.
arXiv:2608. 01692v1 Announce Type: new Abstract: We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.
arXiv:2605. 29920v2 Announce Type: replace Abstract: We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models.
arXiv:2606. 31576v1 Announce Type: new Abstract: The use of ordinary and stochastic differential equations has led to substantial progress in generative machine learning with applications to, for example, image, video and biomolecule generation.
arXiv:2608. 03117v1 Announce Type: new Abstract: The performance of generative diffusion models is determined by the choice of the reference diffusion process connecting the empirical and prior distributions.