  The discovery of ultra-high-energy (UHE) neutrinos has the potential to offer
unique insight into fundamental questions. To capitalize on the upcoming
opportunity provided by new UHE neutrino telescopes, we provide
state-of-the-art forecasts of the discovery of a diffuse flux of UHE neutrinos
over the next 10-20 years, focusing on neutrino radio-detection in the planned
IceCube-Gen2 detector. We use state-of-the-art flux predictions and detector
modeling. We find that, even under conservative analysis choices, most
benchmark UHE neutrino flux models from the literature may be discovered within
10 years of detector exposure, with many discoverable sooner, and may be
distinguished from each other. Our results demonstrate the transformative
potential of next-generation UHE neutrino telescopes.
