  In the quest to build generative surrogate models as computationally
efficient alternatives to rule-based simulations, the quality of the generated
samples remains a crucial frontier. So far, normalizing flows have been among
the models with the best fidelity. However, as the latent space in such models
is required to have the same dimensionality as the data space, scaling up
normalizing flows to high dimensional datasets is not straightforward. The
prior L2LFlows approach successfully used a series of separate normalizing
flows and sequence of conditioning steps to circumvent this problem. In this
work, we extend L2LFlows to simulate showers with a 9-times larger profile in
the lateral direction. To achieve this, we introduce convolutional layers and
U-Net-type connections, move from masked autoregressive flows to coupling
layers, and demonstrate the successful modelling of showers in the ILD
Electromagnetic Calorimeter as well as Dataset 3 from the public CaloChallenge
dataset.
