We have used an all-optical photoluminescence-imaging technique to mea
sure excitonic transport in three types of GaAs structures in which th
e excitonic transitions vary from allowed direct-gap excitons to forbi
dden, doubly-indirect Type-II excitons. We find remarkable differences
in the transport properties of these excitons. Our studies show that
bulk free-exciton transport exhibits an anomalous laser power-dependen
t diffusivity, whereas quasi-2D interfacial excitons and Type-II cross
-interface excitons do not. Additionally, we observe localization of c
ross-interface excitons at the potential disorder induced by the heter
ointerface roughness.