Accurate spallation-neutron source terms are essential for accelerator-driven systems (ADS), yet double-differential cross-section (DDX) data remain sparse, particularly for proton- \(^\text {nat}\) Pb, a benchmark ADS target. We present a data-driven pathway from sparse measurements to dense DDX using a Bayesian tensor model together with a physics-consistent interpolation scheme tailored for ADS source-term construction. A total of 1,727 DDX points for proton– \(^\text {nat}\) Pb, compiled from EXFOR and the literature, spanning eight incident energies (10 MeV–3 GeV) and seven angles (7.5– \(150^\circ\) ), are used jointly to fit the tensor model. Under the selected hyperparameters, the model shows strong in-sample agreement on a logarithmic scale. For data-sparse checks, we compare predictions with the Bertini intranuclear-cascade model in Geant4 (and BERT_HP where available) on common discrete grids: Agreement is close below 10 MeV; in the 20–100 MeV band, where BERT/BERT_HP often underpredict the measurements, our predictions remain physically plausible. To deliver application-ready inputs, we construct a high-resolution dataset via bilinear interpolation in \((E_\text {p},\theta )\) on self-similar energy slices \(\kappa =\ln (E_\text {n}/E_\text {p})\) , evaluated on a regular grid with 1 MeV spacing in \(E_\text {p}\) and \(0.5^\circ\) in \(\theta\) , with a no-extrapolation policy. The interpolants preserve evaporation-like low-energy behavior and forward-peaked high-energy emission while remaining consistent with Geant4 trends. The resulting proton- \(^\text {nat}\) Pb DDX dataset, covering the CiADS design point (500 MeV) and its neighborhood, can be coupled to transport codes (e.g., OpenMC) for anisotropic source-term calculations and can be extended to other targets and reactions.
