Diffusion tensor imaging cannot represent heterogeneous fascicle orientations in one voxel. Various models propose to overcome this limitation. Among them, multi-fascicle models are of great interest to characterize and compare white matter properties. However, existing methods fail to estimate their parameters from conventional diffusion sequences with the desired accuracy. In this paper, we provide a geometric explanation to this problem. We demonstrate that there is a manifold of indistinguishable multi-fascicle models for single-shell data, and that the manifolds for different b-values intersect tangentially at the true underlying model making the estimation very sensitive to noise. To regularize it, we propose to learn a prior over the model parameters from data acquired at several b-values in an external population of subjects. We show that this population-informed prior enables for the first time accurate estimation of multi-fascicle models from single-shell data as commonly acquired in clinical context. The approach is validated on synthetic and in vivo data of healthy subjects and patients with autism. We apply it in population studies of the white matter microstructure in autism spectrum disorder. This approach enables novel investigations from large existing DWI datasets in normal development and in disease.