Purpose: Oscillating gradient spin‐echo (OGSE) diffusion MRI provides information about the microstructure of biological tissues by means of the frequency dependence of the apparent diffusion coefficient (ADC). ADC dependence on OGSE frequency has been explored in numerous rodent studies, but applications in the human brain have been limited and have suffered from low contrast between different frequencies, long scan times, and a limited exploration of the nature of the ADC dependence on frequency. Theory and Methods: Multiple frequency OGSE acquisitions were acquired in healthy subjects at 7T to explore the power‐law frequency dependence of ADC, the "diffusion dispersion." Furthermore, a method for optimizing the estimation of the ADC difference between different OGSE frequencies was developed, which enabled the design of a highly efficient protocol for mapping diffusion dispersion. Results: For the first time, evidence of a linear dependence of ADC on the square root of frequency in healthy human white matter was obtained. Using the optimized protocol, high‐quality, full‐brain maps of apparent diffusion dispersion rate were also demonstrated at an isotropic resolution of 2 mm in a scan time of 6 min. Conclusions: This work sheds light on the nature of diffusion dispersion in the healthy human brain and introduces full‐brain diffusion dispersion mapping at clinically relevant scan times. These advances may lead to new biomarkers of pathology or improved microstructural modeling. [ABSTRACT FROM AUTHOR]