This paper introduces a generative model that minimizes the second‑order Wasserstein loss (W₂) by solving a distribution‑dependent ordinary differential equation (ODE) whose dynamics involve the Kantorovich potential of the true data distribution and its current estimate. The authors prove that the time‑marginal laws of this ODE form a gradient flow for the W₂ loss, converging exponentially to the true data distribution, and propose an Euler scheme that recovers this gradient flow in the limit. An algorithm based on this scheme, combined with persistent training, is shown in experiments to outperform Wasserstein GANs in both low‑ and high‑dimensional settings when the level of persistent training is appropriately increased.
arXiv:2102. 09235v3 Announce Type: replace Abstract: Recent studies revealed the mathematical connection between deep neural networks (DNNs) and dynamic systems.
arXiv:2608.29647v1 Announce Type: new Abstract: To mitigate the time complexity of generative models, one-step generative models have recently emerged through direct mapping from noise to data in a s...
arXiv:2607. 04738v1 Announce Type: cross Abstract: Reconstructing population dynamics is a central problem in the physical and data sciences.
arXiv:2509.19276v2 Announce Type: replace-cross Abstract: Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this t...
Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional.
arXiv:2605.29713v2 Announce Type: replace-cross Abstract: This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence....
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.
arXiv:2410. 02596v2 Announce Type: replace-cross Abstract: Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training algorithms.
arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
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.
arXiv:2606. 10089v1 Announce Type: cross Abstract: In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields.