Differentiable Surrogate for Detector Simulation and Design with Diffusion Models

Abstract: In this work, we present a conditional denoising-diffusion surrogate for electromagnetic calorimeter showers that is trained to generate high-fidelity energy-deposition maps conditioned on key detector and beam parameters. The model employs efficient inference using Denoising Diffusion Implicit Model sampling and is pre-trained on GEANT4 simulations before being adapted to a new calorimeter geometry through Low-Rank Adaptation, requiring only a small post-training dataset. We evaluate physically meaningful observables, including total deposited energy, energy-weighted radius, and shower dispersion, obtaining relative root mean square error values below 2% for representative high-energy cases. This is in line with state-of-the-art calorimeter surrogates which report comparable fidelity on high-level observables. Furthermore, we compare gradients of a reconstruction-based utility function with respect to design parameters between the surrogate and finite-difference references. The diffusion surrogate reproduces the qualitative structure and directional trends of the true utility landscape, providing usable sensitivities for gradient-based optimization. These results show that diffusion-based surrogates can accelerate simulation-driven detector design while enabling differentiable, gradient-informed analysis.