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.
By Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
By Linglingzhi Zhu, Yunqin Zhu, Yao Xie
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.
By Sivaraman Balakrishnan
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:2510. 12636v5 Announce Type: replace-cross Abstract: The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones.
By Jannis Chemseddine, Gregor Kornhardt, Richard Duong, Gabriele Steidl
arXiv:2606. 08113v1 Announce Type: new Abstract: A small Wasserstein distance does not certify that a transformation is admissible.
By Lei Luo, Jian Yang
arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.
By Thejani Gamage, Hyemin Gu, Zhizhen Zhang, Ziyu Chen, Markos Katsoulakis, Luc Rey-Bellet
arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
By Sunder Ram Krishnan
arXiv:2606. 01954v1 Announce Type: new Abstract: Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling.
By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen
The paper introduces a conditional Wasserstein GAN to approximate posterior distributions in compound loss models, conditioning on sufficient statistics, prior mean, coefficient of variation, and mixture weights. A single generator can learn the posteriors for both Poisson intensity and Pareto shape parameters across Gamma, inverse‑Gaussian, and lognormal priors. The authors validate the approach with simulation‑based calibration, analytical comparisons, and extensive MCMC, and apply it to extreme natural catastrophe loss data to generate rolling one‑year posterior predictive distributions and assess tail risk under heavy‑tailed severity and prior uncertainty.
By Aleksandar Arandjelovic, Pavel V. Shevchenko, George Tzougas
arXiv:2607. 24983v1 Announce Type: cross Abstract: Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data.
By Ziwei Zhang, Jonathan Yu-Meng Li, Zhihao Jin
arXiv:2609.27546v1 Announce Type: cross
Abstract: Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution...
By Wei Luo, Neil K. Chada, Shijie Zhang, Lu Yu