In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Generative neural networks map a standard, possibly distribution to a complex high-dimensional distribution, which represents the real world data set. However, a determinate input distribution as well as a specific architecture of neural networks may impose limitations on capturing the diversity in the high dimensional target space. To resolve this difficulty, we propose a training framework that greedily produce a series of generative adversarial networks that incrementally capture the diversity of the target space. We show theoretically and empirically that our training algorithm converges to the theoretically optimal distribution, the projection of the real distribution onto the convex hull of the network's distribution space.
We propose a new method to incrementally train a mixture generative model to approximate the information projection of the real data distribution.