7 papers
Beckmann Transport Models: From Autonomous Flows to One-Step Maps
Lee Cheuk-Kit, Florentin Coeurdoux, Yuyuan Chen +5
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 t…
Generative Modeling via Kernelized Stochastic Interpolants
Florentin Coeurdoux, Etienne Lempereur, Nathanaël Cuvelle-Magar +2
We develop a kernel method for generative modeling within the stochastic interpolant framework, replacing neural network training with linear systems. The drift of the generative S…
Covariance Shrinkage via Stochastic Interpolation
Mathieu Chalvidal, Florentin Coeurdoux, Eric Vanden-Eijnden
We recast classical shrinkage of high-dimensional covariance estimators as empirical risk minimization over a parametric stochastic interpolant between a source and a target distri…
Random Matrix Theory of Early-Stopped Gradient Flow: A Transient BBP Scenario
Florentin Coeurdoux, Grégoire Ferré, Jean-Philippe Bouchaud
Empirical studies of trained models often report a transient regime in which signal is detectable in a finite gradient descent time window before overfitting dominates. We provide…
Probing the Geometry of Diffusion Models with the String Method
Elio Moreau, Florentin Coeurdoux, Grégoire Ferre +1
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited…
Multitask Learning with Stochastic Interpolants
Hugo Negrel, Florentin Coeurdoux, Michael S. Albergo +1
We propose a framework for learning maps between probability distributions that broadly generalizes the time dynamics of flow and diffusion models. To enable this, we generalize st…