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We study a stochastic spatial model of biological competition in which twospecies have the same birth and death rates, but different diffusion constants.In the absence of this difference, the model can be considered as anoff-lattice version of the Voter model and presents similar coarseningproperties. We show that even a relative difference in diffusivity on the orderof a few percent may lead to a strong bias in the coarsening process favoringthe more agile species. We theoretically quantify this selective advantage andpresent analytical formulas for the average growth of the fastest species andits fixation probability.

Selective advantage of diffusing faster