  Understanding the production mechanism of light (anti-)nuclei in high-energy
nuclear collisions and cosmic rays has been a long-standing problem in nuclear
physics. In the present study, we develop a stochastic method to solve the
relativistic kinetic equations for light nuclei production from many-body
reactions with the inclusion of their finite sizes. The present approach gives
an excellent description of the deuteron and helium-3 data from central Au+Au
(Pb+Pb) collisions at $\sqrt{s_{\rm NN}}$ $=$ $200~\rm GeV$ ($2.76~\rm TeV$).
It can also naturally explain their suppressed production in $pp$ collisions at
7 TeV as a result of their finite sizes.
