The orientation-dependent molecular diffusion in the nematic liquid crystal 4-pentyl-4'-cyanobiphenyl is measured to high accuracy. The applied nuclear magnetic resonance method combines multiple-pulse homonuclear dipolar decoupling with pulsed-field-gradient stimulated echo and slice selection. The obtained temperature dependencies of the principal diffusion coefficients are not described by a simple Arrhenius relationship but reflect the decrease of the molecular orientational order close to the nematic-to-isotropic phase transition. The geometric average of the principal diffusion coefficients is continuous with the diffusion coefficient in the isotropic phase. The results are best described in terms of the affine transformation model of diffusion in hard-ellipsoid nematics.