Ion implantation in diamond crystals is widely used both for producing conducting microstructures in the bulk of the material and for creating isolated photon emitters in quantum optics, photonics, cryptography, and biosensorics. The photoluminescence (PL) spectra of helium ion-implanted diamonds are dominated by two sharp emission lines, HR1 and HR2 (from Helium-Related), at ~536 and 560 nm. Here, we report on PL studies of helium-related optical centers in diamonds. Experiments have been carried out on a (110) plate of natural single-crystal type IIa diamonds. The uniform distribution of radiation defects in a 700 nm-thick layer was obtained by ten cycles of multiple-energy (from 24 to 350 kV) helium ion implantation with a total dose of 5 × 1016 cm−2. The diamonds were annealed in steps in a vacuum oven at temperatures from 200 to 1040 °C. It is demonstrated that helium ion implantation in diamonds followed by annealing gives rise to more than a dozen various centers that are observed in the PL spectra in the range of 530–630 nm. The transformations of the PL spectra due to annealing are investigated in detail. The spectral shapes of phonon sidebands are determined for the HR1, HR2, and HR3 bands with ZPLs at ~536, 560, and 577 nm, respectively, and it is shown that these bands are attributed to interstitial-related centers in diamonds. The reported results are important for understanding the structure and properties of helium-related defects in diamonds.