We consider the problem of learning a continuous probability density function from data, a fundamental problem in statistics known as density estimation. It also arises in distributionally robust optimization (DRO), where the goal is to find the worst-case distribution to represent scenario departure from observations. Such a problem is known to be hard in high dimensions and incurs a significant computational challenge. In this talk, I will present a machine learning approach to tackle these challenges, leveraging recent advances in neural-networks-based generative models, which have become popular recently due to their competitive performance in high-dimensional data. We develop a neural ODE flow network called JKO-iFlow, inspired by the Jordan-Kinderleherer-Otto (JKO) scheme, which unfolds the discrete-time dynamic of the Wasserstein gradient flow. Our method can greatly reduce computational costs when achieving competitive performance over existing generative models. The connection of our JKO-iFlow method with proximal gradient descent in the Wasserstein space enables us to prove a density learning guarantee with an exponential convergence rate. Besides density estimation, we also demonstrate that the JKO-flow generative model can be used in various applications, including adversarial learning, robust hypothesis testing, and data-driven differential privacy.