Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, cancer- or energy research. While magnetic resonance methods are the gold standard for quantitative diffusion measurements, they lack sensitivity in resolving and measuring diffusion within individual microstructures. Here, we introduce nitrogen-vacancy (NV) center based nuclear magnetic resonance (NMR) spectroscopy as a novel tool to probe diffusion in individual structures on microscopic length scales. We have developed a novel experimental scheme combining pulsed gradient spin echo (PGSE) with optically detected NV-NMR, which allows for the quantification of molecular diffusion and flow within nano-to-picoliter sample volumes. We demonstrate correlated optical imaging with spatially resolved PGSE NV-NMR experiments to probe anisotropic water diffusion within a model microstructure. Our method will extend the current capabilities of investigating diffusion processes to the microscopic length scale with the potential of probing single-cells, tissue microstructures, or ion mobility in thin film materials for battery applications.