We develop a generalization of the geometric picture for high-energy antiproton (proton)-proton elastic scattering. The eikonal at each impact parameter is considered to have fluctuations about an average value, and is thus characterized by a distribution. A connection to parton branching is made through the specific form of the distribution function for the eikonal. A unified physical theory with significant fluctuations accurately describes the anti p(p)-p data at both ..sqrt..s = 546 GeV and 53 GeV. The fluctuation parameter is remarkably well given by that directly observed in multiparticle production.