Reconstruction of gravitational form factors using generative machine learning

We develop a generative framework based on denoising diffusion for the model-independent reconstruction of hadronic form factors from sparse and noisy data. The generative prior is built from a large ensemble of synthetic curves drawn from ten distinct functional classes rooted in different theoretical approaches to hadron structure. Applied to the proton gravitational form factors A ( t ) , J ( t ) , and D ( t ) , the framework yields nonparametric reconstructions consistent with lattice QCD across the full kinematic range 0 ≤ − t ≤ 2 GeV 2 , remaining robust even when only one or two conditioning points are retained. The densely sampled output enables a direct extraction of the chiral low-energy constants c 8 = − 4.6 ± 0.8 GeV − 1 and c 9 = − 0.61 ± 0.19 GeV − 1 . Using these values at the physical pion mass, we obtain D ( 0 ) = − 4.3 ± 0.8 for the nucleon D -term.