Experiments demonstrate that individual cells that wander stochastically can migrate persistently as a cluster. We show by simulating cells and their interactions that collective migration by omnidirectional cells is a generic phenomenon that can be expected to arise whenever (a) leading and trailing cells migrate randomly, and (b) leading cells are more closely packed than trailing neighbors. The first condition implies that noise is essential to cluster motion, while the second implies that an internal cohesion gradient can drive external motion of a cluster. Unlike other swarming phenomena, we find that this effect is driven by cohesion asymmetry near the leading cell, and motion of interior cells contribute minimally - and in fact interfere with - a cluster's persistent migration.