In biological contexts as diverse as development, apoptosis, and synthetic microbial consortia, collections of cells or sub-cellular components have been shown to overcome the slow signaling speed of simple diffusion by utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule. This collective effect gives rise to fast-traveling diffusive waves. Here, in the context of cell signaling, we show that system dimensionality – the shape of the extracellular medium and the distribution of cells within it – can dramatically affect the wave dynamics, but that these dynamics are insensitive to details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. We further show that cell signaling relays generate much steeper concentration profiles than does simple diffusion, which may facilitate neutrophil chemotaxis.