A foundation model is a machine learning model that has been pre-trained on a large amount of data, Machine learning (ML) methods have been a common and can then be fine-tuned for different downstream ingredient in particle physics research for a long tasks [61]. The idea behind utilizing pre-trained time, with neural networks being applied to object models is that their outputs can significantly enhance identification already in analyses at LEP [1]. Since the performance of downstream tasks, yielding then, the range of applications has grown drastically, better results than if the model were to be trained with ML methods being developed and used for from scratch. While the models mentioned above example in tagging [2-4], anomaly detection [5-8], have focused on exploring different tasks in specific individual reconstruction stages like particle tracking subdomains, like jet physics, a more ambitious goal [9-11] or even full event interpretation and reconstruction eventually would be to develop a foundation model [12]. Another important use case for for all tasks in all subdomains, including for example ML in high energy physics (HEP) is detector simulation.

We present the results of the "Fast Calorimeter Simulation Challenge 2022" -- the CaloChallenge. We study state-of-the-art generative models on four calorimeter shower datasets of increasing dimensionality, ranging from a few hundred voxels to a few tens of thousand voxels. The 31 individual submissions span a wide range of current popular generative architectures, including Variational AutoEncoders (VAEs), Generative Adversarial Networks (GANs), Normalizing Flows, Diffusion models, and models based on Conditional Flow Matching. We compare all submissions in terms of quality of generated calorimeter showers, as well as shower generation time and model size. To assess the quality we use a broad range of different metrics including differences in 1-dimensional histograms of observables, KPD/FPD scores, AUCs of binary classifiers, and the log-posterior of a multiclass classifier. The results of the CaloChallenge provide the most complete and comprehensive survey of cutting-edge approaches to calorimeter fast simulation to date. In addition, our work provides a uniquely detailed perspective on the important problem of how to evaluate generative models. As such, the results presented here should be applicable for other domains that use generative AI and require fast and faithful generation of samples in a large phase space.

In the quest to build generative surrogate models as computationally efficient alternatives to rule-based simulations, the quality of the generated samples remains a crucial frontier. So far, normalizing flows have been among the models with the best fidelity. However, as the latent space in such models is required to have the same dimensionality as the data space, scaling up normalizing flows to high dimensional datasets is not straightforward. The prior L2LFlows approach successfully used a series of separate normalizing flows and sequence of conditioning steps to circumvent this problem. In this work, we extend L2LFlows to simulate showers with a 9-times larger profile in the lateral direction. To achieve this, we introduce convolutional layers and U-Net-type connections, move from masked autoregressive flows to coupling layers, and demonstrate the successful modelling of showers in the ILD Electromagnetic Calorimeter as well as Dataset 3 from the public CaloChallenge dataset.

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 $6\times$ speed-up over Geant4 on a single CPU ($5\times$ over CaloClouds). We further distill the diffusion model into a consistency model allowing for accurate sampling in a single step and resulting in a $46\times$ ($37\times$) speed-up. This constitutes the first application of consistency distillation for the generation of calorimeter showers.

Simulating showers of particles in highly-granular detectors is a key frontier in the application of machine learning to particle physics. Achieving high accuracy and speed with generative machine learning models would enable them to augment traditional simulations and alleviate a major computing constraint. This work achieves a major breakthrough in this task by, for the first time, directly generating a point cloud of a few thousand space points with energy depositions in the detector in 3D space without relying on a fixed-grid structure. This is made possible by two key innovations: i) using recent improvements in generative modeling we apply a diffusion model to generate ii) an initial even higher-resolution point cloud of up to 40, 000 so-called Geant4 steps which is subsequently down-sampled to the desired number of up to 6, 000 space points. We showcase the performance of this approach using the specific example of simulating photon showers in the planned electromagnetic calorimeter of the International Large Detector (ILD) and achieve overall good modeling of physically relevant distributions.