Score-Based Generative Models through the Lens of Wasserstein Proximal Operators

Explore the mathematical foundations of score-based generative models through a rigorous analysis connecting them to Wasserstein proximal operators in this 27-minute conference presentation. Discover how score-based generative models can be understood as entropically regularized Wasserstein proximal operators for cross-entropy, with this connection illuminated through mean-field games theory. Learn about the unique structure of SGM-MFG that allows the Hamilton-Jacobi-Bellman equation alone to characterize score-based generative models, and see how this demonstrates equivalence to an uncontrolled Fokker-Planck equation via Cole-Hopf transform. Examine an interpretable kernel-based model for score functions that enhances SGM performance in terms of both training samples and training time. Gain insights into how the mathematical formulation of kernel-based models, combined with the utilization of terminal conditions in mean-field games, reveals novel perspectives on manifold learning and generalization properties of score-based generative models.