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.
Back to Long Programs
Copyright. All Rights Reserved.