PURPOSE: To achieve high-resolution, three-dimensional (3D) quantitative diffusion-weighted MR spectroscopic imaging (DW-MRSI) for molecule-specific microstructural imaging of the brain. METHODS: We introduced and integrated several innovative acquisition and processing strategies for DW-MRSI: (a) a new double-spin-echo sequence combining selective excitation, bipolar diffusion encoding, rapid spatiospectral sampling, interleaved water spectroscopic imaging data, and a special sparsely sampled echo-volume-imaging (EVI)-based navigator, (b) a rank-constrained time-resolved reconstruction from the EVI data to capture spatially varying phases, (c) a model-based phase correction for DW-MRSI data, and (d) a multi-b-value subspace-based method for water/lipids removal and spatiospectral reconstruction using learned metabolite subspaces, and e) a hybrid subspace and parametric model-based parameter estimation strategy. Phantom and in vivo experiments were performed to validate the proposed method and demonstrate its ability to map metabolite-specific diffusion parameters in 3D. RESULTS: The proposed method generated reproducible metabolite diffusion coefficient estimates, consistent with those from a standard single-voxel DW spectroscopy (SV-DWS) method. High-SNR multi-molecular mean diffusivity (MD) maps can be obtained at a 6.9 CONCLUSION: We demonstrated an unprecedented capability of simultaneous, high-resolution metabolite and diffusion parameter mapping. This imaging capability has strong potential to offer richer molecular and tissue-compartment-specific microstructural information for various clinical and neuroscience applications.