# CaloHadronic: a diffusion model for the generation of hadronic showers

arXiv: https://arxiv.org/abs/2506.21720 · HTML: https://mlsanity.com/paper/2506.21720/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 46 of its 94 references that are in the map.
- First posted on arXiv 26 Jun 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [Score-based Generative Models for Calorimeter Shower Simulation](https://mlsanity.com/paper/2206.11898/) (2022)
- [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)
- [CaloChallenge 2022: A Community Challenge for Fast Calorimeter Simulation](https://mlsanity.com/paper/2410.21611/) (2024)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)

## Built on by (most cited first, 8 of 8)

- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (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)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)
- [GPT-Based Fast Simulation of CLAS12 Detector Hits via Conditional Autoregressive Generation](https://mlsanity.com/paper/2606.16035/) (2026)
- [On the Principles Behind Neural Network Optimizers](https://mlsanity.com/paper/2608.16760/) (2026)
- [Machine learning for the LHC physics program: a 2025-2026 stocktake](https://mlsanity.com/paper/2609.32874/) (2026)

## Abstract (arXiv)

Simulating showers of particles in highly-granular calorimeters is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models can enable them to augment traditional simulations and alleviate a major computing constraint. Recent developments have shown how diffusion based generative shower simulation approaches that do not rely on a fixed structure, but instead generate geometry-independent point clouds, are very efficient. We present a transformer-based extension to previous architectures which were developed for simulating electromagnetic showers in the highly granular electromagnetic calorimeter of the International Large Detector, ILD. The attention mechanism now allows us to generate complex hadronic showers with more pronounced substructure across both the electromagnetic and hadronic calorimeters. This is the first time that machine learning methods are used to holistically generate showers across the electromagnetic and hadronic calorimeter in highly granular imaging calorimeter systems.