The exciton dynamics in monolayer and bulk MoSe2 samples are studied by transient absorption microscopy with a high spatiotemporal resolution. Excitons are injected with a point-like spatial distribution using a tightly focused femtosecond pulse. The spatiotemporal dynamics of these excitons are monitored by measuring transient absorption of a time-delayed and spatially scanned probe pulse. We obtain the exciton diffusion coefficients of 12 ± 3 and 19 ± 2 cm(2) s(-1) and exciton lifetimes of 130 ± 20 and 210 ± 10 ps in the monolayer and bulk samples, respectively. These values are useful for understanding excitons and their interactions with the environment in these structures and potential applications of MoSe2 in optoelectronics and electronics.