Understanding the human brain requires access to its microscopic tissue architecture. Diffusion magnetic resonance imaging (MRI) provides the only noninvasive window into whole-brain microstructure in vivo, yet reliable quantitative mapping remains confined to specialized research settings requiring dense sampling and optimized acquisition protocols. To address this gap, we present a physics-informed generative microstructure network (PIGMENT) that learns a universal generative prior of human brain microstructure and adapts it zero-shot to each participant's measured data to recover subject-specific maps. Trained on 11375 scans spanning multiple sites, vendors, and field strengths, PIGMENT enabled reliable quantitative mapping for tensor, kurtosis, and NODDI models across external datasets from five independent centers. It remains effective where conventional fitting becomes unreliable, recovering meaningful maps from extremely sparse acquisitions while supporting downstream tractography and structural connectivity mapping. PIGMENT estimates demonstrated strong biological validity, preserving submillimeter cortical microarchitectural patterns and early-childhood white matter developmental trajectories from 10-fold accelerated scans. Furthermore, PIGMENT enables reliable quantitative tensor mapping on cost-efficient low-field systems and the extraction of tumor-related biomarkers using ultra-fast clinical protocols. Together, these results establish PIGMENT as a physics-informed foundation model that extends quantitative diffusion MRI into regimes traditionally too sparse, heterogeneous, or clinically constrained for reliable analysis.