# Inverse Autoregressive Flows for Zero Degree Calorimeter fast simulation

arXiv: https://arxiv.org/abs/2512.20346 · HTML: https://mlsanity.com/paper/2512.20346/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)
- [CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds](https://mlsanity.com/paper/2211.15380/) (2022)
- [Inductive Simulation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2305.11934/) (2023)
- [End-to-end Sinkhorn Autoencoder with Noise Generator](https://mlsanity.com/paper/2006.06704/) (2020)
- [Calo-VQ: Vector-Quantized Two-Stage Generative Model in Calorimeter Simulation](https://mlsanity.com/paper/2405.06605/) (2024)
- [Selectively increasing the diversity of GAN-generated samples](https://mlsanity.com/paper/2207.01561/) (2022)
- [Generative Diffusion Models for Fast Simulations of Particle Collisions at CERN](https://mlsanity.com/paper/2406.03233/) (2024)

## Built on by (most cited first, 3 of 3)

- [AllShowers: One model for all calorimeter showers](https://mlsanity.com/paper/2601.11716/) (2026)
- [SPADE: Split-and-Delay Embeddings for Autoregressive High-Granularity Calorimeter Simulation](https://mlsanity.com/paper/2606.11304/) (2026)
- [Fine-tuned Normalizing Flows for ALICE Zero Degree Calorimeter Fast Simulation](https://mlsanity.com/paper/2608.12795/) (2026)

## Abstract (arXiv)

Physics-based machine learning blends traditional science with modern data-driven techniques. Rather than relying exclusively on empirical data or predefined equations, this methodology embeds domain knowledge directly into the learning process, resulting in models that are both more accurate and robust. We leverage this paradigm to accelerate simulations of the Zero Degree Calorimeter (ZDC) of the ALICE experiment at CERN. Our method introduces a novel loss function and an output variability-based scaling mechanism, which enhance the model's capability to accurately represent the spatial distribution and morphology of particle showers in detector outputs while mitigating the influence of rare artefacts on the training. Leveraging Normalizing Flows (NFs) in a teacher-student generative framework, we demonstrate that our approach not only outperforms classic data-driven model assimilation but also yields models that are 421 times faster than existing NF implementations in ZDC simulation literature.