Generation of Imaging Air Cherenkov Telescope images using Diffusion Models

Abstract

Substantial amounts of air-shower simulations are needed to derive the instrument response for analyzing Imaging Air Cherenkov Telescope (IACT) data. This process is both computationally intensive and requires repetition under varying observation conditions, due to detector aging, changes in the atmosphere, or the instrument hardware. Generative models offer an efficient alternative, significantly accelerating simulations while compactly storing extensive simulation libraries, and providing a differentiable surrogate model of the instrument. However, their applicability has so far been limited in gamma-ray astronomy, particularly for modeling hadronic showers that dominate the background and exhibit significant intrinsic fluctuations that are challenging to model. In this study, we present the first application of score-based diffusion models to generate monoscopic $γ$-ray and proton shower images with nearly 2,000 pixels and benchmark the performance against Wasserstein GANs using H.E.S.S. simulations. We examine quality using both low-level parameters and well-established shower-shape observables, and assess analysis readiness via state-of-the-art $γ$-hadron separation. While GAN-based approaches can reproduce $γ$-ray showers with high fidelity, they fail to generate proton events of comparable quality, leading to a measurable degradation in analysis performance. In contrast, score-based diffusion modles achieve significantly superior quality for $γ$-ray and proton showers, accurately reproducing high-level correlations and generating events that are statistically indistinguishable from simulations at the analysis level. These results establish diffusion-based models as the first analysis-ready surrogate model of a single IACT, opening new prospects for fast instrument response generation, detector optimization, and connected downstream tasks.

Figures (16)

• Figure 1: Various stages of the generation process of an IACT image starting from Gaussian noise using a score-based diffusion model. The particle causing the signal is a proton with an energy of 5.5 TeV. The black pixels denote zero-value pixels and brighter pixels denote higher values.
• Figure 2: Sketch of the model training and image generation process of our diffusion model framework. During the model training, the global model learns to predict physical properties characterizing the images using only the primary particle energy as input. The image model learns to generate images from noise, energy, and the physical properties. During the image generation process the models are used together. The image model takes the information that the global model predicts alongside the input energy and noise to generate the final IACT image.
• Figure 3: IACT $\gamma$-ray (left) and proton (right) image with applied tail-cuts cleaning using thresholds of 9 p.e. and 16 p.e. Included in both images is the reconstructed Hillas ellipse, its major axis, and center, respectively. The black pixels denote zero-value pixels.
• Figure 4: Comparison of four $\gamma$-ray IACT images obtained from MC simulations (top), the WGAN (middle), and the SBDM (bottom). The simulated images are hand-picked to show various characteristics of air showers induced by $\gamma$-rays. The WGAN and SBDM images are the next neighbors of the simulated images in the mean-squared-error pixel space. Note that a 4/7 tail-cuts cleaning with the extension of four rows is applied, and black pixels denote pixels that do not contain any signal.
• Figure 5: Comparison of the image sizes (top left), number of signal pixels (top middle), the pixel values (top right), and the pixel occupancy (bottom) for the $\gamma$-ray dataset from the MC simulation, the WGAN, and the SBDM. The range of the color bar of the relative pixel occupancy is set to show $\pm 5\sigma$ around the mean value of the MC image.