Conventional diffusion MRI yields voxel‐averaged parameters that suffer from ambiguities for heterogeneous anisotropic materials such as brain tissue. Using principles from solid‐state NMR spectroscopy, we have previously introduced the shape of the diffusion encoding tensor as a separate acquisition dimension that disentangles isotropic and anisotropic contributions to the observed diffusivities, thereby allowing for unconstrained data inversion into diffusion tensor distributions with “size,” “shape,” and orientation dimensions. Here we combine our recent non‐parametric data inversion algorithm and data acquisition protocol with an imaging pulse sequence to demonstrate spatial mapping of diffusion tensor distributions using a previously developed composite phantom with multiple isotropic and anisotropic components. We propose a compact format for visualizing two‐dimensional arrays of the distributions, new scalar parameters quantifying intra‐voxel heterogeneity, and a binning procedure giving maps of all relevant parameters for each of the components resolved in the multidimensional distribution space.