Towards Universal Wasserstein Barycenters through Flow Matching
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
The Flow has not summarised this story yet — read it at arXiv AI.
arXiv:2510. 04602v4 Announce Type: replace-cross Abstract: Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space.
arXiv:2505. 06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns.
arXiv:2606. 10089v1 Announce Type: cross Abstract: In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields.
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
arXiv:2511. 17812v3 Announce Type: replace-cross Abstract: Flow matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets.
arXiv:2606. 16610v1 Announce Type: cross Abstract: Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood.