  We explore the use of normalizing flows to emulate Monte Carlo detector
simulations of photon showers in a high-granularity electromagnetic calorimeter
prototype for the International Large Detector (ILD). Our proposed method --
which we refer to as "Layer-to-Layer-Flows" (L$2$LFlows) -- is an evolution of
the CaloFlow architecture adapted to a higher-dimensional setting (30 layers of
$10\times 10$ voxels each). The main innovation of L$2$LFlows consists of
introducing $30$ separate normalizing flows, one for each layer of the
calorimeter, where each flow is conditioned on the previous five layers in
order to learn the layer-to-layer correlations. We compare our results to the
BIB-AE, a state-of-the-art generative network trained on the same dataset and
find our model has a significantly improved fidelity.
