Purpose: We propose a new generalized diffusion tensor imaging (GDTI) experimental design and analysis framework for efficiently measuring orientationally averaged diffusionweighted images (DWIs), which remove bulk signal modulations attributed to diffusion anisotropy and quantify isotropic higher-order diffusion tensors (HOT). We illustrate how this framework accelerates the clinical measurement of rotationinvariant tissue microstructural parameters derived from HOT, such as the HOT-Trace and the mean t-kurtosis. Theory and Methods: For a large range of b-values, we compare orientationally averaged DWIs measured with high angular resolution diffusion imaging to those obtained with the proposed isotropic GDTI (IGDTI) experimental design. We compare rotation-invariant microstructural parameters measured with IGDTI to those derived from HOTs measured explicitly with GDTI.