Herein we present a quantitative noise analysis of diffraction enhanced imaging (DEI), an x-ray imaging method that produces absorption and refraction images, with inherent immunity to wide-angle scatter. DEI can be used for planar imaging or computed tomography. DEI produces excellent images, but requires an x-ray source of very high power; therefore, it has principally been confined to synchrotron studies. Clinical systems currently under development using conventional x-ray sources will be photon-limited. Therefore, it is important that the noise properties of DEI be understood. We derive mathematical expressions for the noise statistics of DEI images, and show that the original formulation of DEI, given by Chapman, et al, is the maximum-likelihood solution of the image-estimation problem for the case of Poisson noise. However, we find that the standard DEI solution is only unbiased under particular conditions, which must be obeyed if good results are to be achieved. We also present the results of applying various noise-reduction filters, which we found to be very effective in reducing noise variance while introducing little bias.