Simulations provide the crucial link between theoretical descriptions and experimental observations in the physical sciences. In experimental particle physics, a complex ecosystem of tools exists to describe fundamental processes or the interactions of particles with detectors. The high computational cost associated with producing precise simulations in sufficient quantities --- e.g. for the upcoming data-taking phase of the Large Hadron Collider (LHC) or future colliders --- motivates research into more computationally efficient solutions. Using generative machine learning models to amplify the statistics of a given dataset is an especially promising direction. However, the simulation of realistic showers in a highly granular detector remains a daunting problem due to the large number of cells, values spanning many orders of magnitude, and the overall sparsity of data. This contribution advances the state of the art in two key directions: Firstly, we present a precise generative model for the fast simulation of hadronic showers in a highly granular hadronic calorimeter. Secondly, we compare the achieved simulation quality before and after interfacing with a so-called particle-flow-based reconstruction algorithm. Together, these bring generative models one step closer to practical applications.