Overview of Generative Modelling

Suppose $(\mathsf{Y}, \mathcal{Y}, \nu)$ is a probability space, and we consider $\nu$ as being the “data” distribution. Let $Y_1, \ldots, Y_n$ be IID random variables taking values in $\mathsf{Y}$ and being distributed according to $\nu$, which we consider as our observed dataset. The task of generative modelling is to learn an approximation of $\nu$ such that we can sample from it and generate realistic samples.