Diffusion-based magnetic resonance imaging holds the potential to non-invasively demonstrate cellular-scale structural properties of brain. This method was applied to fixed baboon brains ranging from 90 to 185 days gestational age to characterize the changes in diffusion properties associated with brain development. Within each image voxel, a probability-theory-based approach was employed to choose, from a group of analytic equations, the one that best expressed water displacements. The resulting expressions contain eight or fewer adjustable parameters, indicating that relatively simple expressions are sufficient to obtain a complete description of the diffusion MRI signal in developing brain. The measured diffusion parameters changed systematically with gestational age, reflecting the rich underlying microstructural changes that take place during this developmental period. These changes closely parallel those of live, developing human brain. The information obtained from this primate model of cerebral microstructure is directly applicable to studies of human development.