Abstract: Short-range repulsion governs the dynamic behavior of matter across length scales, from atoms to animals. As the density increases, the dynamics transition from nearest-neighbor to many-body interactions, posing a challenge for an analytical description. Here, we use theory, simulations, and experiments to show that a suspension of particles with short-range repulsion spreads compactly. Unlike the diffusive boundary of a spreading drop of Brownian particles, a compact expansion is characterized by a density profile that is strictly zero beyond a cutoff distance. Starting from the microscopic interactions, we derive an effective, non-linear diffusion equation and find that the dynamics exhibit two distinct transitions: (1) when very dense, particle-particle interactions extend beyond nearest neighbors, and the ensemble grows in a self-similar fashion as t1/4. (2) At lower densities, nearest-neighbor interactions dominate, and the expansion slows to logarithmic growth. We examine the second regime experimentally by monitoring the expansion of a dense suspension of charge-stabilized colloids. Using simulations of thousands of particles, we observe the continuous crossover between the self-similar and the logarithmic dynamics. Our results are general and robust, with practical implications in engineering and pharmaceutical industries, where suspensions must operate at extreme densities.