the first part of the talk, we demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. We establish connections between MFGs and major classes of flow- and diffusion-based generative models by deriving continuous-time normalizing flows, score-based models, and Wasserstein gradient flows through different choices of particle dynamics and cost functions. Second, from a UQ perspective, relying on a new Wasserstein uncertainty propagation theorem, we show that score-based generative models (SGMs) are provably robust to multiple sources of error in their practical implementation. The regularizing properties of Hamilton-Jacobi-Bellman equations in the MFG formulation of SGMs are the key ingredient of this analysis.