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Generative Modeling through Koopman Spectral Analysis: An Operator-Theoretic Perspective
Yuanchao Xu, Fengyi Li, Masahiro Fujisawa +3
We propose Koopman Spectral Wasserstein Gradient Descent (KSWGD), a particle-based generative modeling framework that learns the Langevin generator via Koopman theory and integrate…
Conformal Prediction for Generative Models via Adaptive Cluster-Based Density Estimation
Qidong Yang, Qianyu Julie Zhu, Jonathan Giezendanner +3
Conditional generative models map input variables to complex, high-dimensional distributions, enabling realistic sample generation in a diverse set of domains. A critical challenge…
Localized Diffusion Models
Georg A. Gottwald, Shuigen Liu, Youssef Marzouk +2
Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers…
Distribution learning via neural differential equations: minimal energy regularization and approximation theory
Youssef Marzouk, Zhi Ren, Jakob Zech
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g…