  Generative AI is a fast-growing area of research offering various avenues for
exploration in high-energy nuclear physics. In this work, we explore the use of
generative models for simulating electron-proton collisions relevant to
experiments like CEBAF and the future Electron-Ion Collider (EIC). These
experiments play a critical role in advancing our understanding of nucleons and
nuclei in terms of quark and gluon degrees of freedom. The use of generative
models for simulating collider events faces several challenges such as the
sparsity of the data, the presence of global or event-wide constraints, and
steeply falling particle distributions. In this work, we focus on the
implementation of diffusion models for the simulation of electron-proton
scattering events at EIC energies. Our results demonstrate that diffusion
models can accurately reproduce relevant observables such as momentum
distributions and correlations of particles, momentum sum rules, and the
leading electron kinematics, all of which are of particular interest in
electron-proton collisions. Although the sampling process is relatively slow
compared to other machine learning architectures, we find diffusion models can
generate high-quality samples. We foresee various applications of our work
including inference for nuclear structure, interpretable generative machine
learning, and searches of physics beyond the Standard Model.
