48 citations · 413 across the 59 of their papers we have counts for
6 papers · 2 filters
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang
We introduce a novel Wasserstein-1 () path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bo…
Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flows
Hyemin Gu, Markos A. Katsoulakis, Luc Rey-Bellet +1
We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of…
Score-based generative models are provably robust: an uncertainty quantification perspective
Nikiforos Mimikos-Stamatopoulos, Benjamin J. Zhang, Markos A. Katsoulakis
Through an uncertainty quantification (UQ) perspective, we show that score-based generative models (SGMs) are provably robust to the multiple sources of error in practical implemen…
Nonlinear denoising score matching for enhanced learning of structured distributions
Jeremiah Birrell, Markos A. Katsoulakis, Luc Rey-Bellet +2
We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlin…
Robust Generative Learning with Lipschitz-Regularized -Divergences Allows Minimal Assumptions on Target Distributions
Ziyu Chen, Hyemin Gu, Markos A. Katsoulakis +2
This paper demonstrates the robustness of Lipschitz-regularized -divergences as objective functionals in generative modeling, showing they enable stable learning across a wide r…
Wasserstein proximal operators describe score-based generative models and resolve memorization
Benjamin J. Zhang, Siting Liu, Wuchen Li +2
We focus on the fundamental mathematical structure of score-based generative models (SGMs). We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) and demonstr…