Diffusion magnetic resonance imaging (dMRI) has become increasingly relevant in clinical research and neuroscience. It is commonly carried out using the ultra-fast MRI acquisition technique Echo-Planar Imaging (EPI). While offering crucial reduction of acquisition times, two limitations of EPI are distortions due to varying magnetic susceptibilities of the object being imaged and its limited spatial resolution. In the recent years progress has been made both for susceptibility artefact correction and increasing of spatial resolution using image processing and reconstruction methods. However, so far, the interplay between both problems has not been studied and super-resolution techniques could only be applied along one axis, the slice-select direction, limiting the potential gain in spatial resolution. In this work we describe a new method for joint susceptibility artefact correction and super-resolution in EPI-MRI that can be used to increase resolution in all three spatial dimensions and in particular increase in-plane resolutions. The key idea is to reconstruct a distortion-free, high-resolution image from a number of low-resolution EPI data that are deformed in different directions. Numerical results on dMRI data of a human brain indicate that this technique has the potential to provide for the first time in-vivo dMRI at mesoscopic spatial resolution (i.e. 500μm); a spatial resolution that could bridge the gap between white-matter information from ex-vivo histology (≈1μm) and in-vivo dMRI (≈2000μm).