Recorded 15 July 2025. Siting Liu of the University of California, Riverside, presents "Score-Based Generative Models through the Lens of Wasserstein Proximal Operators" at IPAM's Sampling, Inference, and Data-Driven Physical Modeling in Scientific Machine Learning Workshop. Abstract: In this presentation, I will discuss the essence of score-based generative models (SGMs) as entropically regularized Wasserstein proximal operators (WPO) for cross-entropy, elucidating this connection through mean-field games (MFG). The unique structure of SGM-MFG allows the HJB equation alone to characterize SGMs, demonstrated to be equivalent to an uncontrolled Fokker-Planck equation via a Cole-Hopf transform. Furthermore, leveraging the mathematical framework, we introduce an interpretable kernel-based model for the score functions, enhancing the performance of SGMs in terms of training samples and training time. The mathematical formulation of the new kernel-based models, in conjunction with the utilization of the terminal condition of the MFG, unveils novel insights into the manifold learning and generalization properties of SGMs. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/sampling-inference-and-data-driven-physical-modeling-in-scientific-machine-learning-2/