# CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds

arXiv: https://arxiv.org/abs/2211.15380 · HTML: https://mlsanity.com/paper/2211.15380/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [The Malicious Use of Artificial Intelligence: Forecasting, Prevention, and Mitigation](https://mlsanity.com/paper/1802.07228/) (2018)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Normalizing Flows on Riemannian Manifolds](https://mlsanity.com/paper/1611.02304/) (2016)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [Rectangular Flows for Manifold Learning](https://mlsanity.com/paper/2106.01413/) (2021)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows](https://mlsanity.com/paper/2106.05275/) (2021)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Density estimation on low-dimensional manifolds: an inflation-deflation approach](https://mlsanity.com/paper/2105.12152/) (2021)

## Built on by (most cited first, 28 of 28)

- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models](https://mlsanity.com/paper/2406.03537/) (2024)
- [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)
- [Comparison of Point Cloud and Image-based Models for Calorimeter Fast Simulation](https://mlsanity.com/paper/2307.04780/) (2023)
- [OmniJet-αC: Learning point cloud calorimeter simulations using generative transformers](https://mlsanity.com/paper/2501.05534/) (2025)
- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [CaloHadronic: a diffusion model for the generation of hadronic showers](https://mlsanity.com/paper/2506.21720/) (2025)
- [Calorimeter shower superresolution](https://mlsanity.com/paper/2308.11700/) (2023)
- [PIPPIN: Generating variable length full events from partons](https://mlsanity.com/paper/2406.13074/) (2024)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [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)
- [On Convolutions, Intrinsic Dimension, and Diffusion Models](https://mlsanity.com/paper/2506.20705/) (2025)
- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (2025)
- [Inverse Autoregressive Flows for Zero Degree Calorimeter fast simulation](https://mlsanity.com/paper/2512.20346/) (2025)
- [AllShowers: One model for all calorimeter showers](https://mlsanity.com/paper/2601.11716/) (2026)
- [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)
- [A First Full Physics Benchmark for Highly Granular Calorimeter Surrogates](https://mlsanity.com/paper/2511.17293/) (2025)
- [A universal vision transformer for fast calorimeter simulations](https://mlsanity.com/paper/2601.05289/) (2026)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)
- [ExpertSim: Fast Particle Detector Simulation Using Mixture-of-Generative-Experts](https://mlsanity.com/paper/2508.20991/) (2025)
- [GPT-Based Fast Simulation of CLAS12 Detector Hits via Conditional Autoregressive Generation](https://mlsanity.com/paper/2606.16035/) (2026)

## Abstract (arXiv)

Precision measurements and new physics searches at the Large Hadron Collider require efficient simulations of particle propagation and interactions within the detectors. The most computationally expensive simulations involve calorimeter showers. Advances in deep generative modelling - particularly in the realm of high-dimensional data - have opened the possibility of generating realistic calorimeter showers orders of magnitude more quickly than physics-based simulation. However, the high-dimensional representation of showers belies the relative simplicity and structure of the underlying physical laws. This phenomenon is yet another example of the manifold hypothesis from machine learning, which states that high-dimensional data is supported on low-dimensional manifolds. We thus propose modelling calorimeter showers first by learning their manifold structure, and then estimating the density of data across this manifold. Learning manifold structure reduces the dimensionality of the data, which enables fast training and generation when compared with competing methods.