  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 $L_X= 0.36\pm
0.02 \; \mu$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 $L_{X^D}=1.5\pm 0.02 \;\mu$m.
