  In this paper, we introduce a convenient framework for studying (adversarial)
generative models from a statistical perspective. It consists in modeling the
generative device as a smooth transformation of the unit hypercube of a
dimension that is much smaller than that of the ambient space and measuring the
quality of the generative model by means of an integral probability metric. In
the particular case of integral probability metric defined through a smoothness
class, we establish a risk bound quantifying the role of various parameters. In
particular, it clearly shows the impact of dimension reduction on the error of
the generative model.
