A series of inorganic/organic composite films exhibiting high thermal stability and high thermal diffusivity was prepared from five different grades of flake-shaped hexagonal boron nitride (hBN) and aromatic polyimides (PIs). Thermal diffusivities along the out-of-plane (D(perpendicular)) and in-plane (D//) directions of hBN/PI films were separately measured and analyzed in terms of particle size, shape, concentration, and orientation, as well as molecular structures of rigid and flexible PI matrices. hBN/PI films filled with large flake-shaped particles exhibited a large anisotropy in D(perpendicular) and D// due to the strong in-plane orientation of heat-conducting basal plane of hBN, while smaller anisotropy was observed in composites with small flakes and aggregates which tend to orient less in the in-plane direction during film processing. The anisotropic thermal diffusion property observed in hBN/PI films exhibited strong correlation with the orientation of hBN particles estimated using scanning electron micrographs (SEM) and wide-angle X-ray diffraction. Moreover, composites of hBN with a rigid-rod PI matrix exhibited much larger anisotropy in D(perpendicular) and D// than flexible PI-composites, reflecting the effect of the rigid and densely packed PI chains preferentially orienting parallel to the film plane. The thermal conductivities of the hBN/rigid-rod PI films were estimated as 5.4 and 17.5 W/m·K along the out-of-plane and in-plane directions, respectively, which is one of the largest values ever reported.