# CaloClouds II: Ultra-Fast Geometry-Independent Highly-Granular Calorimeter Simulation

arXiv: https://arxiv.org/abs/2309.05704 · HTML: https://mlsanity.com/paper/2309.05704/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 104 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 30 of 52)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Fast Sampling of Diffusion Models via Operator Learning](https://mlsanity.com/paper/2211.13449/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [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)
- [Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis](https://mlsanity.com/paper/1701.05927/) (2017)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [Particle Cloud Generation with Message Passing Generative Adversarial Networks](https://mlsanity.com/paper/2106.11535/) (2021)

## Built on by (most cited first, 20 of 20)

- [OmniJet-α: The first cross-task foundation model for particle physics](https://mlsanity.com/paper/2403.05618/) (2024)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [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)
- [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)
- [Foundation models for high-energy physics](https://mlsanity.com/paper/2509.21434/) (2025)
- [Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion](https://mlsanity.com/paper/2404.14332/) (2024)
- [CaloHadronic: a diffusion model for the generation of hadronic showers](https://mlsanity.com/paper/2506.21720/) (2025)
- [Flow Matching Beyond Kinematics: Generating Jets with Particle-ID and Trajectory Displacement Information](https://mlsanity.com/paper/2312.00123/) (2023)
- [A Comprehensive Evaluation of Generative Models in Calorimeter Shower Simulation](https://mlsanity.com/paper/2406.12898/) (2024)
- [Calibrating Bayesian Generative Machine Learning for Bayesiamplification](https://mlsanity.com/paper/2408.00838/) (2024)
- [BUFF: Boosted Decision Tree based Ultra-Fast Flow matching](https://mlsanity.com/paper/2404.18219/) (2024)
- [Physics Instrument Design with Reinforcement Learning](https://mlsanity.com/paper/2412.10237/) (2024)
- [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)
- [A First Full Physics Benchmark for Highly Granular Calorimeter Surrogates](https://mlsanity.com/paper/2511.17293/) (2025)
- [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)
- [Jet Image Generation in High Energy Physics Using Diffusion Models](https://mlsanity.com/paper/2508.00250/) (2025)

## Abstract (arXiv)

Fast simulation of the energy depositions in high-granular detectors is needed for future collider experiments with ever-increasing luminosities. Generative machine learning (ML) models have been shown to speed up and augment the traditional simulation chain in physics analysis. However, the majority of previous efforts were limited to models relying on fixed, regular detector readout geometries. A major advancement is the recently introduced CaloClouds model, a geometry-independent diffusion model, which generates calorimeter showers as point clouds for the electromagnetic calorimeter of the envisioned International Large Detector (ILD). In this work, we introduce CaloClouds II which features a number of key improvements. This includes continuous time score-based modelling, which allows for a 25-step sampling with comparable fidelity to CaloClouds while yielding a 6× speed-up over Geant4 on a single CPU (5× over CaloClouds). We further distill the diffusion model into a consistency model allowing for accurate sampling in a single step and resulting in a 46× (37× over CaloClouds) speed-up. This constitutes the first application of consistency distillation for the generation of calorimeter showers.