The quasiparticle bands of diamond, a prototype covalent insulator, are herein studied by means of a wavefunction electronic-structure theory, with emphasis on the nature of the correlation hole around a bare particle. Short-range correlations are in such a system conveniently described by using a real-space representation and many-body techniques from ab initio quantum chemistry. To account for long-range polarization effects, on the other hand, we adopt the approximation of a dielectric continuum. Having as "uncorrelated" reference the Hartree-Fock band structure, the post-Hartree-Fock treatment is carried out in terms of localized Wannier functions derived from the Hartree-Fock solution. The computed correlation-induced corrections to the relevant real-space matrix elements are important and give rise to a strong reduction, in the range of 50%, of the initial Hartree-Fock gap. While our final results for the indirect and direct gaps, 5.4 and 6.9 eV, respectively, compare very well with the experimental data, the width of the valence band comes out by 10% to 15% too large as compared to experiment. This overestimation of the valence-band width appears to be related to size-consistency effects in the configuration-interaction correlation treatment.