Gaussian Mixture Model(GMM) is one of the distribution models that can produce highly accurate estimates of any density. Inspired by Fourier transform, we purposed a Gaussian Mixture Model Expansion (GMME) that expand any density with a set of base Gaussian distributions. We demonstrate that using GMME to approximate any form of distribution, the approximation error is constrained. Based on our concept, we create a learning algorithm and compare it directly to the Wasserstein approach for use with neural networks. In this talk we will briefly walk through our work and showcase some applications.