Wasserstein proximal operators are non-expansive under total or 2-base generalized geodesic convexity and locally 1/2-Hölder under ordinary generalized geodesic convexity.
arXiv preprint arXiv:2509.03506 (2025)
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Introduces Wasserstein-on-Wasserstein flow matching that realizes metameasure flows via nested Wasserstein geometry and scalable sliced/linear approximations for generative modeling of transport plans.
Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.
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On the stability of proximal operators in Wasserstein spaces under different notions of convexity
Wasserstein proximal operators are non-expansive under total or 2-base generalized geodesic convexity and locally 1/2-Hölder under ordinary generalized geodesic convexity.
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Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once
Introduces Wasserstein-on-Wasserstein flow matching that realizes metameasure flows via nested Wasserstein geometry and scalable sliced/linear approximations for generative modeling of transport plans.
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Adapted Optimal Transport between Filtered Gaussian Processes
Adapted optimal transport on filtered Gaussian processes reduces to a constrained Procrustes problem between Cholesky factors, yielding explicit martingale projections and asymptotic equivalence among bicausal couplings.