We consider the physical nature of the self-diusion of water molecules in tissue and explore how (Nuclear) Magnetic Resonance (MR) imaging may be used as a means of measuring the rate of diusion in vivo. A discussion is presented on how these techniques may be implemented as a non-invasive means of assessing the response of tumours to novel therapeutics including some of the basic advantages and disadvan- tages when compared to other methods. The physical basis and mathematical models for diusion are considered together with models for the distribution of the diusion co- ecient including a L evy distributed model. Using a L evy distributed diusion model, we develop a novel algorithm for the purpose of improving the signal-to-noise ratio of MR images.