In this paper we present a method for reconstructing diffusion-weighted MRI data on regular grids from scattered data. The proposed method has the advantage that no specific diffusion model needs to be assumed. Previous work assume the tensor model, but this is not suitable under certain conditions like intravoxel orientational heterogeneity (IVOH). Data reconstruction is particularly important when studying the fetal brain in utero, since registration methods applied for movement and distortion correction produce scattered data in spatial and diffusion domains. We propose the use of a groupwise registration method, and a dual spatio-angular interpolation by using radial basis functions (RBF). Leave-one-out experiments performed on adult data showed a high accuracy of the method. The application to fetal data showed an improvement in the quality of the sequences according to objective criteria based on fractional anisotropy (FA) maps, and differences in the tractography results.