# PC-Droid: Faster diffusion and improved quality for particle cloud generation

arXiv: https://arxiv.org/abs/2307.06836 · HTML: https://mlsanity.com/paper/2307.06836/

## 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 37 of its 62 references that are in the map.
- First posted on arXiv 13 Jul 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 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [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)
- [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)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications](https://mlsanity.com/paper/2001.06937/) (2020)
- [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)
- [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)
- [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)
- [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)
- [Controlling Physical Attributes in GAN-Accelerated Simulation of Electromagnetic Calorimeters](https://mlsanity.com/paper/1711.08813/) (2017)
- [EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets](https://mlsanity.com/paper/2301.08128/) (2023)
- [End-To-End Latent Variational Diffusion Models for Inverse Problems in High Energy Physics](https://mlsanity.com/paper/2305.10399/) (2023)

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

- [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)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [Flow Matching Beyond Kinematics: Generating Jets with Particle-ID and Trajectory Displacement Information](https://mlsanity.com/paper/2312.00123/) (2023)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [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)
- [Lantern: Conflict-Aware Gradient Blending for Physics-Guided Diffusion Models in Calorimeter Simulation](https://mlsanity.com/paper/2607.25060/) (2026)

## Abstract (arXiv)

Building on the success of PC-JeDi we introduce PC-Droid, a substantially improved diffusion model for the generation of jet particle clouds. By leveraging a new diffusion formulation, studying more recent integration solvers, and training on all jet types simultaneously, we are able to achieve state-of-the-art performance for all types of jets across all evaluation metrics. We study the trade-off between generation speed and quality by comparing two attention based architectures, as well as the potential of consistency distillation to reduce the number of diffusion steps. Both the faster architecture and consistency models demonstrate performance surpassing many competing models, with generation time up to two orders of magnitude faster than PC-JeDi and three orders of magnitude faster than Delphes.