Tentative observations of cosmic-ray antihelium by the AMS-02 collaboration have re-energized the quest to use antinuclei to search for physics beyond the standard model. However, our transition to a data-driven era requires more accurate models of the expected astrophysical antinuclei fluxes. We use a state-of-the-art cosmic-ray propagation model, fit to high-precision antiproton and cosmic-ray nuclei (B, Be, Li) data, to constrain the antinuclei flux from both astrophysical and dark matter annihilation models. We show that astrophysical sources are capable of producing 𝒪(1) antideuteron events and 𝒪(0.1) antihelium-3 events over 15 years of AMS-02 observations. Standard dark matter models could potentially produce higher levels of these antinuclei, but showing a different energy-dependence. Given the uncertainties in these models, dark matter annihilation is still the most promising candidate to explain preliminary AMS-02 results. Meanwhile, any robust detection of antihelium-4 events would require more novel dark matter model building or a new astrophysical production mechanism.