Safety
Towards Universal Wasserstein Barycenters through Flow Matching
arXiv:2609.38547v1 Announce Type: cross Abstract: Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstei
arXiv:2609.38547v1 Announce Type: cross Abstract: Defining a weighted mean over probability measures under probability metrics is a central tool in probabilistic machine learning. Under the Wasserstein metric, these are called Wasserstein barycenters. While most approaches compute barycenters for a fixed weight vector, approximating the whole family of barycenters over the simplex, which we call the Wasserstein simplex, remains underexplored. We refer to this problem as Universal Barycenter Approximation, and propose exttt{BaryFM}, a flow matching model transporting the marginal measures into any barycenter in the Wasserstein simplex. Once trained, the network can draw samples from measures in the Wasserstein simplex through an ordinary differential equation. We validate our method on 4 downstream tasks: domain adaptation, generalization, Bayesian posterior aggregation and algorithmic fairness. exttt{BaryFM} achieves the best average rank among 15 competing methods across 10 domain adaptation benchmarks, matching or surpassing non-universal solvers.
Related
- On Variance Reduction in Learning Mean Flows
- Distillation for Efficient Multitask Manipulation Policies via Conditional Flow Matching
- Refinement-based Flow Policy Optimization
- Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching
Source: arXiv cs.AI | 2026-10-01