Hugo Lavenant

The flow map of the Fokker-Planck equation: not an optimal transport map, but almost? 
Abstract: A few years ago we proved with Filippo Santambrogio that the flow map of the Fokker-Planck equation cannot, generically, be an optimal transport map. I will discuss numerical experiments showing nevertheless that it looks very close to an optimal transport map, and a few tentative explanations of this intriguing observation. 

Giacomo Zanella

Error Bounds and Optimal Schedules for Masked Diffusion models
Abstract: Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some bias in the sampling distribution. We study the resulting computation-vs-accuracy trade-off, providing general error bounds (in relative entropy) that depend only on the average number of tokens generated per iteration and are independent of the data dimensionality (i.e. sequence length). We then investigate the gains obtained by using non-constant schedule sizes and identify the optimal schedule as a function of the so-called information profile of the data distribution. Our results support the empirical success of MDMs and allow for a simple and principled data-driven optimization of schedule sizes. The talk is based on joint work with Hugo Lavenant, available at https://arxiv.org/abs/2510.25544.

For further information please contact elisur.magrini@unibocconi.it