The correlations of nucleons with small relative momenta and the deuteron or antideuteron formation are both due to the final state interactions. We calculate in parallel the neutron-proton correlation function and the (anti-)deuteron formation rate. The two quantities are expressed through the space-time parameters of the particle source created in nucleus-nucleus collisions. In the case of baryon reach sources, the nucleons are emitted from the whole source volume while the antinucleons dominantly from the surface due to the antinucleon absorption in the baryon environment. Thus, the shape of the antinucleon source is different from the nucleon one, and consequently the antideuteron formation rate is substantially smaller than that one of deuterons. The correlation function is shown to satisfy the sum rule, which, in particular, connects the number of correlated neutron-proton pairs to the number of produced deuterons. The sum rule applications are briefly discussed.