In this talk we report on a novel approach for the integration of scattering cross sections and the generation of partonic event samples in high-energy physics. It is based on an importance sampling algorithm which includes the use of neural networks in order to overcome typical shortcomings of conventional approaches. At the same time, a potential pitfall of neural networks in the context of phase-space sampling, namely mappings that are non-bijective after trainings with finite data sets, is avoided by employing the technique of Neural Importance Sampling. With this, full phase-space coverage and the correct reproduction of the target distribution is guaranteed even for limited training statistics. We study the performance gains of our implementation for a prototypical high-energy physics example, namely gluon scattering into three- and four-gluon final states.