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Generation of simulated detector response to collision products is crucial todata analysis in particle physics, but computationally very expensive. Onesubdetector, the calorimeter, dominates the computational time due to the highgranularity of its cells and complexity of the interactions. Generative modelscan provide more rapid sample production, but currently require significanteffort to optimize performance for specific detector geometries, oftenrequiring many models to describe the varying cell sizes and arrangements,without the ability to generalize to other geometries. We develop a$\textit{geometry-aware}$ autoregressive model, which learns how thecalorimeter response varies with geometry, and is capable of generatingsimulated responses to unseen geometries without additional training. Thegeometry-aware model outperforms a baseline unaware model by over $50\%$ inseveral metrics such as the Wasserstein distance between the generated and thetrue distributions of key quantities which summarize the simulated response. Asingle geometry-aware model could replace the hundreds of generative modelscurrently designed for calorimeter simulation by physicists analyzing datacollected at the Large Hadron Collider. This proof-of-concept study motivatesthe design of a foundational model that will be a crucial tool for the study offuture detectors, dramatically reducing the large upfront investment usuallyneeded to develop generative calorimeter models.

Generalizing to new geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation