Random motion within the cytoplasm gives rise to molecular diffusion; this motion is essential to many biological processes. However, in addition to thermal Brownian motion, the cytoplasm also undergoes constant agitation caused by the activity of molecular motors and other nonequilibrium cellular processes. Here, we discuss recent work that suggests this activity can give rise to cytoplasmic motion that has the appearance of diffusion but is significantly enhanced in its magnitude and which can play an important biological role, particularly in cytoskeletal assembly.