# EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion

arXiv: https://arxiv.org/abs/2310.00049 · HTML: https://mlsanity.com/paper/2310.00049/

## Key facts

- Cited by 17 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 43 of its 92 references that are in the map.
- First posted on arXiv 29 Sep 2023.

## 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 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [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)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [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)
- [Particle Cloud Generation with Message Passing Generative Adversarial Networks](https://mlsanity.com/paper/2106.11535/) (2021)
- [Calorimetry with Deep Learning: Particle Simulation and Reconstruction for Collider Physics](https://mlsanity.com/paper/1912.06794/) (2019)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [LHC analysis-specific datasets with Generative Adversarial Networks](https://mlsanity.com/paper/1901.05282/) (2019)
- [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)

## Built on by (most cited first, 17 of 17)

- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [Improving new physics searches with diffusion models for event observables and jet constituents](https://mlsanity.com/paper/2312.10130/) (2023)
- [Full Event Particle-Level Unfolding with Variable-Length Latent Variational Diffusion](https://mlsanity.com/paper/2404.14332/) (2024)
- [EventFlow: Forecasting Temporal Point Processes with Flow Matching](https://mlsanity.com/paper/2410.07430/) (2024)
- [Flow Matching Beyond Kinematics: Generating Jets with Particle-ID and Trajectory Displacement Information](https://mlsanity.com/paper/2312.00123/) (2023)
- [PIPPIN: Generating variable length full events from partons](https://mlsanity.com/paper/2406.13074/) (2024)
- [Generative Unfolding with Distribution Mapping](https://mlsanity.com/paper/2411.02495/) (2024)
- [Calibrating Bayesian Generative Machine Learning for Bayesiamplification](https://mlsanity.com/paper/2408.00838/) (2024)
- [SURFing to the Fundamental Limit of Jet Tagging](https://mlsanity.com/paper/2511.15779/) (2025)
- [DeepTreeGANv2: Iterative Pooling of Point Clouds](https://mlsanity.com/paper/2312.00042/) (2023)
- [SIGMA: Single Interpolated Generative Model for Anomalies](https://mlsanity.com/paper/2410.20537/) (2024)
- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Variational inference for pile-up removal at hadron colliders with diffusion models](https://mlsanity.com/paper/2410.22074/) (2024)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Multimodal Generative Flows for LHC Jets](https://mlsanity.com/paper/2509.01736/) (2025)
- [Generative models on phase space](https://mlsanity.com/paper/2604.02415/) (2026)
- [Learning Standard Model structure from LHC data with Riemannian flow matching](https://mlsanity.com/paper/2607.16144/) (2026)

## Abstract (arXiv)

Jets at the LHC, typically consisting of a large number of highly correlated particles, are a fascinating laboratory for deep generative modeling. In this paper, we present two novel methods that generate LHC jets as point clouds efficiently and accurately. We introduce epcjedi, which combines score-matching diffusion models with the Equivariant Point Cloud (EPiC) architecture based on the deep sets framework. This model offers a much faster alternative to previous transformer-based diffusion models without reducing the quality of the generated jets. In addition, we introduce epcfm, the first permutation equivariant continuous normalizing flow (CNF) for particle cloud generation. This model is trained with it flow-matching, a scalable and easy-to-train objective based on optimal transport that directly regresses the vector fields connecting the Gaussian noise prior to the data distribution. Our experiments demonstrate that epcjedi and epcfm both achieve state-of-the-art performance on the top-quark JetNet datasets whilst maintaining fast generation speed. Most notably, we find that the epcfm model consistently outperforms all the other generative models considered here across every metric. Finally, we also introduce two new particle cloud performance metrics: the first based on the Kullback-Leibler divergence between feature distributions, the second is the negative log-posterior of a multi-model ParticleNet classifier.