High-energy hadronic collisions generate environments characterized by temperatures above 100 MeV (refs.  1,2), about 100,000 times hotter than the centre of the Sun. At present, it is therefore unclear how light (anti)nuclei with mass number A of a few units, such as the deuteron, 3He or 4He, each bound by only a few MeV, can emerge from these collisions 3,4. Here, the ALICE Collaboration reports that deuteron-pion momentum correlations in proton-proton (pp) collisions provide model-independent evidence that about 90% of the observed (anti)deuterons are produced in nuclear reactions 5 following the decay of short-lived resonances, such as the Δ(1232). These findings, obtained by the ALICE Collaboration at the Large Hadron Collider, resolve a gap in our understanding of nucleosynthesis in ultrarelativistic hadronic collisions. Apart from offering insights on how (anti)nuclei are formed in hadronic collisions, the results can be used in the modelling of the production of light and heavy nuclei in cosmic rays 6 and dark-matter decays 7,8.