We have combined spatially-resolved steady-state micro-photoluminescence ($mu$PL) with time-resolved photoluminescence (TRPL) to investigate the exciton diffusion in a WSe$_2$ monolayer encapsulated with hexagonal boron nitride (hBN). At 300 K, we extract an exciton diffusion length $L_X= 0.36pm 0.02 ; mu$m and an exciton diffusion coefficient of $D_X=14.5 pm 2;mbox{cm}^2$/s. This represents a nearly 10-fold increase in the effective mobility of excitons with respect to several previously reported values on nonencapsulated samples. At cryogenic temperatures, the high optical quality of these samples has allowed us to discriminate the diffusion of the different exciton species : bright and dark neutral excitons, as well as charged excitons. The longer lifetime of dark neutral excitons yields a larger diffusion length of $L_{X^D}=1.5pm 0.02 ;mu$m.
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