We present a new ultra-high b-value diffusion magnetic resonance imaging (dMRI) methodology, Quasi-Diffusion Imaging (QDI). The QDI technique includes a tensor representation of the dMRI data. We show that high contrast to noise images representing standard and non-Gaussian diffusion measures are obtainable in 1 to 4 minutes. QDI entropy maps show pathological contrast similar to Diffusional Kurtosis Imaging (DKI) in stroke and brain tumours. In addition, QDI overcomes the b-value limitations of DKI.