The study of spatial patterns in the distribution of organisms is a central issue in ecology. Here we address the question of whether predator–prey interactions can induce nonuniform distributions. We study how diffusion affects the stability of predator–prey coexistence equilibria and show a new difference between ratio- and prey-dependent models. Recently, Peter Abrams and Lev Ginzburg reviewed the controversial issue of what kind of function better describes the rate of prey consumption by an average predator, the so-called “predator functional response.” Here, we focus on reaction-diffusion predator–prey models with and without predator dependence in the functional response. We show that classical prey-dependent models cannot give rise to spatial structures through diffusion-driven instabilities; however, predator-dependent models with the same degree of complexity can. The origin of predator dependence in the rate of prey consumption is the mutual interference between predators. Therefore, we show that this mechanism can generate patchiness in a homogeneous environment under certain conditions of trophic interaction and predator–prey relative diffusion.