# Even Faster Simulations with Flow Matching: A Study of Zero Degree Calorimeter Responses

arXiv: https://arxiv.org/abs/2507.18811 · HTML: https://mlsanity.com/paper/2507.18811/

## Key facts

- Cited by 2 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 20 of its 39 references that are in the map.
- First posted on arXiv 24 Jul 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, 20 of 20)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [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)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [CaloMan: Fast generation of calorimeter showers with density estimation on learned manifolds](https://mlsanity.com/paper/2211.15380/) (2022)
- [End-to-end Sinkhorn Autoencoder with Noise Generator](https://mlsanity.com/paper/2006.06704/) (2020)
- [Variational Autoencoders for Jet Simulation](https://mlsanity.com/paper/2009.04842/) (2020)
- [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)
- [Machine Learning methods for simulating particle response in the Zero Degree Calorimeter at the ALICE experiment, CERN](https://mlsanity.com/paper/2306.13606/) (2023)
- [Scaling Up Diffusion and Flow-based XGBoost Models](https://mlsanity.com/paper/2408.16046/) (2024)
- [Applying generative neural networks for fast simulations of the ALICE (CERN) experiment](https://mlsanity.com/paper/2407.16704/) (2024)

## Built on by (most cited first, 2 of 2)

- [ExpertSim: Fast Particle Detector Simulation Using Mixture-of-Generative-Experts](https://mlsanity.com/paper/2508.20991/) (2025)
- [Fine-tuned Normalizing Flows for ALICE Zero Degree Calorimeter Fast Simulation](https://mlsanity.com/paper/2608.12795/) (2026)

## Abstract (arXiv)

Recent advances in generative neural networks, particularly flow matching (FM), have enabled the generation of high-fidelity samples while significantly reducing computational costs. A promising application of these models is accelerating simulations in high-energy physics (HEP), helping research institutions meet their increasing computational demands. In this work, we leverage FM to develop surrogate models for fast simulations of zero degree calorimeters in the ALICE experiment. We present an effective training strategy that enables the training of fast generative models with an exceptionally low number of parameters. This approach achieves state-of-the-art simulation fidelity for both neutron (ZN) and proton (ZP) detectors, while offering substantial reductions in computational costs compared to existing methods. Our FM model achieves a Wasserstein distance of 1.27 for the ZN simulation with an inference time of 0.46 ms per sample, compared to the current best of 1.20 with an inference time of approximately 109 ms. The latent FM model further improves the inference speed, reducing the sampling time to 0.026 ms per sample, with a minimal trade-off in accuracy. Similarly, our approach achieves a Wasserstein distance of 1.30 for the ZP simulation, outperforming the current best of 2.08. The source code is available at https://github.com/m-wojnar/faster_zdc.