We have used the diffusion quantum Monte Carlo method to calculate the energy band of the two-dimensional homogeneous electron gas (HEG), and hence we have obtained the quasiparticle effective mass and the occupied bandwidth. We find that the effective mass in the paramagnetic HEG increases significantly when the density is lowered, whereas it decreases in the fully ferromagnetic HEG. Our calculations therefore support the conclusions of recent experimental studies [ Y.-W. Tan et al. Phys. Rev. Lett. 94 016405 (2005); M. Padmanabhan et al. Phys. Rev. Lett. 101 026402 (2008); T. Gokmen et al. Phys. Rev. B 79 195311 (2009)]. We compare our calculated effective masses with other theoretical results and experimental measurements in the literature.