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 non-parametric reconstructions consistent with lattice QCD across the full kinematic range $0\le -t\le 2~\mathrm{GeV}^{2}$, 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 $c_8=-4.6\pm 0.8~\mathrm{GeV}^{-1}$ and $c_9=-0.61\pm 0.19~\mathrm{GeV}^{-1}$. Using these values at the physical pion mass, we obtain $D(0)=-4.3\pm 0.8$ for the nucleon $D$-term.