This paper addresses detector response simulations, which are essential for understanding the inner workings of particle collisions at CERN's Large Hadron Collider (LHC). Because conventional statistical Monte Carlo methods are computationally expensive and place significant strain on CERN's computing grid, this study proposes a generative machine learning approach for efficient simulations. To address the significant variation in data distributions across simulations, which is difficult to capture with conventional methods, we propose ExpertSim, a deep learning simulation approach tailored to the ALICE experiment's zero-degree calorimeter. ExpertSim uses a Mixture of Generative Experts architecture to specialize each expert in simulating a different subset of the data, thereby improving accuracy and speed. It offers speed improvements over conventional Monte Carlo methods, and the code is available on GitHub.