8 papers
Expected Batch Optimal Transport Plans and Consequences for Flow Matching
Samuel Boïté, Julie Delon, Kimia Nadjahi
Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like cou…
Tessellations of Semi-Discrete Flow Matching
Emile Pierret, Johannes Hertrich, Samuel Hurault +1
We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported on finitely many points. This semi-discrete regime is th…
Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport
Samuel Boïté, Eloi Tanguy, Julie Delon +2
The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such as Gaussian Mixture Models (GMMs). Des…
Robust Barycenters of Persistence Diagrams
Keanu Sisouk, Eloi Tanguy, Julie Delon +1
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic…
Sliced Transport Plans
Eloi Tanguy, Laetitia Chapel, Julie Delon
Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein di…
On the Relation between Rectified Flows and Optimal Transport
Johannes Hertrich, Antonin Chambolle, Julie Delon
This paper investigates the connections between rectified flows, flow matching, and optimal transport. Flow matching is a recent approach to learning generative models by estimatin…
A User's Guide to Sampling Strategies for Sliced Optimal Transport
Keanu Sisouk, Julie Delon, Julien Tierny
This paper serves as a user's guide to sampling strategies for sliced optimal transport. We provide reminders and additional regularity results on the Sliced Wasserstein distance.…
Computing Barycentres of Measures for Generic Transport Costs
Eloi Tanguy, Julie Delon, Nathaël Gozlan
Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is…