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The active galactic nuclei (AGNs) are widely believed to be one of thepromising acceleration sites of ultrahigh-energy cosmic rays (CRs).Essentially, AGNs are powered by the gravitational energy of matter falling tosupermassive black holes. However, the conversion efficiency of gravitationalto kinetic energy of CRs in AGNs, which is defined as baryon loading factor$\eta_p$, is not well known yet. After being accelerated, high-energy CRs couldescape the host galaxy and enter the intra-cluster medium (ICM). These CRs canbe confined within the galaxy cluster and produce $\gamma$-rays and neutrinosthrough proton-proton collisions with the ICM. In this paper, we study thediffusion of CRs in galaxy clusters and calculate the diffuse neutrino fluxfrom galaxy cluster population. Using the latest upper limits on the cumulativeunresolved TeV-PeV neutrino flux from galaxy clusters posed by the IceCubeNeutrino Observatory, we derive the upper limit of the average baryon loadingfactor as $\eta_{p,\mathrm{grav}} \lesssim 2 \times 10^{-3} - 0.1$ for thepopulation of galaxy clusters. This constraint is more stringent than the oneobtained from $\gamma$-ray observation on the Coma cluster.

Constraining baryon loading efficiency of AGNs with diffuse neutrino flux from galaxy clusters