Structural similarity has emerged as a promising tool in mapping the network organization of an individual, living human brain. Here, we propose diffusion similarity networks (DSNs), which employ rotationally invariant spherical harmonic features derived from diffusion magnetic resonance imaging (dMRI), to map gray matter structural organization. Compared to prior approaches, DSNs showed clearer laminar, cytoarchitectural, and micro-architectural organization; greater sensitivity to age, cognition, and sex; higher heritability in a large dataset of healthy young adults; and straightforward extension to non-cortical regions. We show DSNs are correlated with functional, structural, and gene expression connectomes and their gradients align with the sensory-fugal and sensorimotor-association axes of the cerebral cortex, including neuronal oscillatory dynamics, metabolism, immunity, and dopaminergic and glutaminergic receptor densities. DSNs can be easily integrated into conventional dMRI analysis, adding information complementary to structural white matter connectivity, and could prove useful in investigating a wide array of neurological and psychiatric conditions.