The simulation of the passage of particles through the detectors of the Large Hadron Collider (LHC) is a core component of any physics analysis. However, a detailed and accurate simulation of the detector response using the Geant4 toolkit is a time and CPU consuming process. This is especially intensified with the large number of simulated events, typical physics analysis need. This thesis documents Machine Learning (ML) based alternatives for a faster simulation of the showering of particles in the ATLAS calorimeter. An ML approach that extends current parametrized simulation is also proposed. The work presented in this thesis follows three main stages: data preprocessing, ML model design, validation and integration into the ATLAS simulation framework. For data preprocessing, the calorimeter cell information is used to derive a suitable data structure. A finer granularity of voxels is then used to better capture the structure of the shower and extend the range of energy and the calorimeter regions. In the preprocessing stage, an innovative ML technique is introduced to automatically learn the optimal structure of the data. The resulting structure is general enough to be compatible with any particle energy and detector region. Once the data is preprocessed and an adapted structure is defined, a Variational AutoEncoder (VAE) termed FastCaloVSim learns to reproduce the showering of particles in the ATLAS calorimeter. A new, physics inspired, loss function is proposed to accurately map the shower energy, the total energy deposited per calorimeter layer and the total energy deposited in all the layers. Furthermore, the VAE is designed as a conditional model, i.e. the learning is conditioned on the pseudorapidity region of the calorimeter as well as the energy of the particle. The model performance is evaluated both as a standalone algorithm and as part of the ATLAS simulation framework. The last stage of this work describes the integration of FastCaloVSim into Athena, the ATLAS simulation framework, allowing further validation of the overall simulation pipeline.