Confocal histology provides an opportunity to establish intra-voxel fiber orientation distributions that can be used to quantitatively assess the biological relevance of diffusion weighted MRI models, e.g., constrained spherical deconvolution (CSD). Here, we apply deep learning to investigate the potential of single shell diffusion weighted MRI to explain histologically observed fiber orientation distributions (FOD) and compare the derived deep learning model with a leading CSD approach. This study (1) demonstrates that there exists additional information in the diffusion signal that is not currently exploited by CSD, and (2) provides an illustrative data-driven model that makes use of this information.