We develop an island dynamics model that employs the level-set technique to describe epitaxial growth. The island boundaries evolve with a velocity that is obtained from solving the diffusion equation for the spatially varying adatom concentration. Islands are nucleated on the surface at a rate that is determined by the ad-atom density. Scaled island size distributions in the submonolayer aggregation regime are compared with those obtained from a kinetic Monte Carlo (KMC) simulation for irreversible as well as reversible aggregation. Excellent agreement is obtained. We identify spatial fluctuations in the seeding of islands as an essential source of noise. We then discuss extensions to the multilayer growth regime.