Conditional Optimal Transport on Function Spaces

Conditional optimal transport provides a framework for representing conditional measures through block-triangular Monge maps. This work develops constrained optimal transport problems and their Kantorovich relaxations in separable infinite-dimensional function spaces, extending triangular transport theory beyond finite-dimensional settings and allowing for general cost functions.

The framework is tailored to Bayesian inference, where conditioning maps describe the transformation from a prior to a posterior distribution. The paper establishes regularity estimates for these maps and demonstrates numerical applications to amortized and likelihood-free inference of functional parameters.

See Conditional Optimal Transport on Function Spaces for details.