Normalizing Flows for High-Dimensional Detector Simulations

We would like to thank the referees for their reports. In particular, we appreciated the detailed report from Referee 2. Our aim for a discussion of meaningful features in calorimeter showers, rather than presenting a large list of figures, greatly benefit from their comments.
We additionally publish the sample in a Zenodo repository with the full set of high-level observables studied.
In light of the extremely encouraging reports from the referees and the promising results, we believe our manuscript meets the criteria for the publication in Scipost Physics.

Main comments:
Regarding the main comments from the referees, section 4.5 now contains a comparison to similar normalizing flows and to a diffusion model in terms of shower generation time and accuracy.
We added a timing comparison and the classifier AUC for high- and low-level features.
We did not perform and in-depth ablation study because of resource constraints. We expanded the appendices with a discussion on the hyperparameters selection and the small grid search done.

Report 1
See main comments.

Report 2

We adopted almost all the text improvements suggested by the referee. We kept the usage of "networks" when explicitly referring to a model defined by a neural network.

Abstract
We extended the abstract with the bottom line of our results.

Introduction
We added a paragraph on the effort done in ATLAS and CMS on fast detector simulations.
The claim is now supported by Sec.4.5 and the appendix on the CaloGAN dataset.

Dataset
We adopted all the suggested changes.

CaloINN
We expanded the text describing the INN, including the scaling aspect with input dimensionality. We also include a new schematic representation of the INN workflow.
We tagged the current state of the Github repo, which only contains refactorizations of the code at the time of submission.

VAE+INN
We added a VAE+INN flowchart and the motivation for a kernel-based encoding/decoding step.

Results
We clarified the first paragraph on photon showers.
We moved the inclusive set of high-level observables to the appendices. As suggested, we show and discuss three incident energies. The layers are chosen such that we discuss where there is the largest energy deposition.
We adopt the same scheme for the pion showers.

For dataset 2, we divided the high-level feature figures in the three E_inc windows (1-10), (10-100), (100-1000) GeV and selected only one layer to discuss the networks.
To avoid overcrowding the paper with figures, we have not done the same for dataset 3 but we included all the histograms in the published Zenodo repository.

We added a timing comparison in Table 3, the high-level classifier in Table 4, and the approximate training time on our cluster in the text.

We clarified the comparison between the INN and the VAE+INN throughout the text.

Conclusion
In the conclusions we expanded the discussion of the performance of our networks on all the studied metrics.
We comment on the observed differences between photon showers in dataset 1 and the electrons in dataset 2.
We give an outlook of what can be improved and directions for future works.

We updated all the references.

Report 3

VAE+INN
1-2 See main comment

3 We expanded the discussion on the selection of the beta parameter. The small value used ensures that the latent space is compact and therefore learnable by the latent INN.

4 We added citations to the beta-VAE and other latent models.