# CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows

arXiv: https://arxiv.org/abs/2110.11377 · HTML: https://mlsanity.com/paper/2110.11377/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 21 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [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)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [ClariNet: Parallel Wave Generation in End-to-End Text-to-Speech](https://mlsanity.com/paper/1807.07281/) (2018)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Calorimetry with Deep Learning: Particle Simulation and Reconstruction for Collider Physics](https://mlsanity.com/paper/1912.06794/) (2019)
- [Controlling Physical Attributes in GAN-Accelerated Simulation of Electromagnetic Calorimeters](https://mlsanity.com/paper/1711.08813/) (2017)
- [DCTRGAN: Improving the Precision of Generative Models with Reweighting](https://mlsanity.com/paper/2009.03796/) (2020)
- [Probability density distillation with generative adversarial networks for high-quality parallel waveform generation](https://mlsanity.com/paper/1904.04472/) (2019)
- [Distilling the Knowledge from Conditional Normalizing Flows](https://mlsanity.com/paper/2106.12699/) (2021)

## Built on by (most cited first, 30 of 34)

- [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)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [Ultra-High-Resolution Detector Simulation with Intra-Event Aware GAN and Self-Supervised Relational Reasoning](https://mlsanity.com/paper/2303.08046/) (2023)
- [EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets](https://mlsanity.com/paper/2301.08128/) (2023)
- [Inductive Simulation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2305.11934/) (2023)
- [CaloClouds II: Ultra-Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2309.05704/) (2023)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [New directions for surrogate models and differentiable programming for High Energy Physics detector simulation](https://mlsanity.com/paper/2203.08806/) (2022)
- [Comparison of Point Cloud and Image-based Models for Calorimeter Fast Simulation](https://mlsanity.com/paper/2307.04780/) (2023)
- [Calo-VQ: Vector-Quantized Two-Stage Generative Model in Calorimeter Simulation](https://mlsanity.com/paper/2405.06605/) (2024)
- [CaloFlow for CaloChallenge Dataset 1](https://mlsanity.com/paper/2210.14245/) (2022)
- [High-dimensional and Permutation Invariant Anomaly Detection](https://mlsanity.com/paper/2306.03933/) (2023)
- [nu-Flows: Conditional Neutrino Regression](https://mlsanity.com/paper/2207.00664/) (2022)
- [PC-Droid: Faster diffusion and improved quality for particle cloud generation](https://mlsanity.com/paper/2307.06836/) (2023)
- [Unifying Simulation and Inference with Normalizing Flows](https://mlsanity.com/paper/2404.18992/) (2024)
- [PIPPIN: Generating variable length full events from partons](https://mlsanity.com/paper/2406.13074/) (2024)
- [Comparison of Affine and Rational Quadratic Spline Coupling and Autoregressive Flows through Robust Statistical Tests](https://mlsanity.com/paper/2302.12024/) (2023)
- [ELSA -- Enhanced latent spaces for improved collider simulations](https://mlsanity.com/paper/2305.07696/) (2023)
- [Generalizing to new geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation](https://mlsanity.com/paper/2305.11531/) (2023)
- [A Comprehensive Evaluation of Generative Models in Calorimeter Shower Simulation](https://mlsanity.com/paper/2406.12898/) (2024)
- [Scaling Up Diffusion and Flow-based XGBoost Models](https://mlsanity.com/paper/2408.16046/) (2024)
- [BUFF: Boosted Decision Tree based Ultra-Fast Flow matching](https://mlsanity.com/paper/2404.18219/) (2024)
- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (2025)
- [ColliderML: The First Release of an OpenDataDetector High-Luminosity Physics Benchmark Dataset](https://mlsanity.com/paper/2512.15230/) (2025)
- [Generalizable Foundation Models for Calorimetry via Mixtures-of-Experts and Parameter Efficient Fine Tuning](https://mlsanity.com/paper/2603.28804/) (2026)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [Even Faster Simulations with Flow Matching: A Study of Zero Degree Calorimeter Responses](https://mlsanity.com/paper/2507.18811/) (2025)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)

## Abstract (arXiv)

Recently, we introduced CaloFlow, a high-fidelity generative model for GEANT4 calorimeter shower emulation based on normalizing flows. Here, we present CaloFlow v2, an improvement on our original framework that speeds up shower generation by a further factor of 500 relative to the original. The improvement is based on a technique called Probability Density Distillation, originally developed for speech synthesis in the ML literature, and which we develop further by introducing a set of powerful new loss terms. We demonstrate that CaloFlow v2 preserves the same high fidelity of the original using qualitative (average images, histograms of high level features) and quantitative (classifier metric between GEANT4 and generated samples) measures. The result is a generative model for calorimeter showers that matches the state-of-the-art in speed (a factor of 104 faster than GEANT4) and greatly surpasses the previous state-of-the-art in fidelity.