Explore deep generative models and their application to uncertainty quantification in function approximation and partial differential equation (PDE) problems through this 58-minute conference talk by Xuhui Meng presented at ICBS2025. Delve into advanced computational methods that leverage deep learning architectures to address uncertainty in mathematical modeling, examining how generative models can provide robust solutions for complex function approximation tasks and PDE-based problems. Learn about cutting-edge techniques that combine probabilistic modeling with deep neural networks to quantify and manage uncertainty in scientific computing applications, gaining insights into the theoretical foundations and practical implementations of these sophisticated approaches for handling uncertainty in mathematical and computational contexts.