► We study the hypothesis that GRBs are the main sources of UHE CRs. ► Our analysis focuses on UHE CR emission in the form of neutrons produced in photo-pion interactions. ► We calculate the associated neutrino spectra by a fit to HiRes data. ► We show that these diffuse neutrino fluxes are challenged by recent upper limits from IceCube. ► This serves as a probe of viable GRB sources in this UHE CR scenario. Gamma ray burst (GRB) fireballs provide one of very few astrophysical environments where one can contemplate the acceleration of cosmic rays to energies that exceed 10 20 eV. The assumption that GRBs are the sources of the observed cosmic rays generates a calculable flux of neutrinos produced when the protons interact with fireball photons. With data taken during construction IceCube has already reached a sensitivity to observe neutrinos produced in temporal coincidence with individual GRBs provided that they are the sources of the observed extra-galactic cosmic rays. We here point out that the GRB origin of cosmic rays is also challenged by the IceCube upper limit on a possible diffuse flux of cosmic neutrinos which should not be exceeded by the flux produced by all GRB over Hubble time. Our alternative approach has the advantage of directly relating the diffuse flux produced by all GRBs to measurements of the cosmic ray flux. It also generates both the neutrino flux produced by the sources and the associated cosmogenic neutrino flux in a synergetic way.