In this talk, we will introduce a Normalizing field flow model (NFF) to quantify uncertainty propagation in a uniļ¬ed framework for forward, inverse and mixed stochastic problems based on scattered measurements. We first build the NFF model for stochastic field by constructing a bijective transformation between Gaussian random filed and the target stochastic field. Then we train the invertible networks by maximizing the sum of the log-likelihood. Furthermore, to solve the SDEs, we encode the known physics, i.e., the form of the stochastic differential equation (SDE), into the architecture of NFF model and learn the unknown stochastic terms in the equations from data. We will demonstrate the performance of the new NFF model with several numerical examples. This is joint work with Hao Wu and Tao Zhou.