Acquisition of a series of anisotropically oversampled acquisitions (so-called anisotropic "snapshots") and reconstruction in the image space has recently been proposed to increase the spatial resolution in diffusion weighted imaging (DWI), providing a theoretical 8x acceleration at equal signal-to-noise ratio (SNR) compared to conventional dense k-space sampling. However, in most works, each DW image is reconstructed separately and the fact that the DW images constitute different views of the same anatomy is ignored. In addition, current approaches are limited by their inability to reconstruct a high resolution (HR) acquisition from snapshots with different subsets of diffusion gradients: an isotropic HR gradient image cannot be reconstructed if one .of its anisotropic snapshots is missing, for example due to intra-scan motion, even if other snapshots for this gradient were successfully acquired. In this work, we propose a novel multi-snapshot DWI reconstruction technique that simultaneously achieves HR reconstruction and local tissue model estimation while enabling reconstruction from snapshots containing different subsets of diffusion gradients, providing increased robustness to patient motion and potential for acceleration. Our approach is formalized as a joint probabilistic model with missing observations, from which interactions between missing snapshots, HR reconstruction and a generic tissue model naturally emerge. We evaluate our approach with synthetic simulations, simulated multi-snapshot scenario and in vivo multi-snapshot imaging. We show that (1) our combined approach ultimately provides both better HR reconstruction and better tissue model estimation and (2) the error in the case of missing snapshots can be quantified. Our novel multi-snapshot technique will enable improved high spatial characterization of the brain connectivity and microstructure in vivo.