The paper introduces multifidelity techniques for building triangular transport maps when high‑fidelity data are limited but low‑fidelity data are plentiful. Two strategies are proposed: a hierarchical approach that composes maps across fidelity levels, and a non‑hierarchical method that uses monotonicity‑preserving corrections to incorporate low‑fidelity information. Numerical tests show these methods outperform single‑fidelity transport and, when applied to amortized simulation‑based inference, improve conditional sampling and uncertainty quantification in data‑scarce regimes.
arXiv:2609.37122v1 Announce Type: new Abstract: Triangular transport maps provide a flexible approach to sampling-based probabilistic modeling, including density estimation, generative modeling, and...
arXiv:2606. 30574v1 Announce Type: new Abstract: Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map.
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2606. 02515v1 Announce Type: new Abstract: Optimal transport (OT) provides a principled framework for mapping between probability distributions.
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
arXiv:2606. 14023v1 Announce Type: cross Abstract: Optimal Transport has become recently a powerful method for domain adaptation by aligning source and target distributions.
arXiv:2606. 05327v1 Announce Type: new Abstract: Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions.
arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv:2609.37424v1 Announce Type: cross Abstract: Optimal Transport (OT) provides a principled framework for learning transformations between probability distributions from unpaired samples. In many...
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.