Net evaporation depends on diffusion, but the initial event behind any given molecule leaving a liquid is not diffusion. In any material, including liquids, there is a statistical distribution of particle speeds. read more
I usually believe that it is a pure diffusion process: the saturated pressure of liquid at the liquid vapor interface is higher than the partial pressure of vapor in the ambient, and this pressure difference makes the liquid evaporate. However, I also know that evaporation absorbs heat. read more