LHC physics is a unique field in the sense that we compare vast and highly complex data sets with precise first-principles predictions. Generative neural networks can supplement these simulations and come with conceptional advantages. I will show how flow-based invertible networks can provide precision simulations with uncertainty estimates and a high level of control through a new, GAN-inspired architecture. In addition, I will discuss how such networks can invert event simulations and unfold detector simulations or the QCD parton shower in a mathemacially consistent manner.