Propagation of light-emitting quasiparticles is of central importance across the fields of condensed matter physics and nanomaterials science. We experimentally demonstrate diffusion of excitons in the presence of a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. Light emission from tightly bound exciton states in electrically gated WSe2 monolayer is detected using spatially and temporally resolved microscopy. The measurements reveal a nonmonotonic dependence of the exciton diffusion coefficient on the charge carrier density in both electron and hole doped regimes. Supported by analytical theory describing exciton-carrier interactions in a dissipative system, we identify distinct regimes of elastic scattering and quasiparticle formation determining exciton diffusion. The crossover region exhibits a highly unusual behavior of an increasing diffusion coefficient with increasing carrier densities. Temperature-dependent diffusion measurements further reveal characteristic signatures of freely propagating excitonic complexes dressed by free charges with effective mobilities up to 3 × 103 cm2/(V s).