The detection of very high-energy neutrinos by IceCube experiment supports the existence of a comparable gamma-ray counterpart from the same cosmic accelerators. Under the likely assumption that the sources of these particles are of extragalactic origin, the emitted photon flux would be significantly absorbed during its propagation over cosmic distances. However, in the presence of photon mixing with ultra-light axion-like-particles (ALPs), this expectation would be strongly modified. Notably, photon-ALP conversions in the host galaxy would produce an ALP flux which propagates unimpeded in the extragalactic space. Then, the back-conversion of ALPs in the Galactic magnetic field leads to a diffuse high-energy photon flux. In this context, the recent detection of the diffuse high-energy photon flux by the Large High Altitude Air Shower Observatory (LHAASO) allows us to exclude at the 95% CL an ALP-photon coupling g(alpha gamma) greater than or similar to 3.9-7.8 x 10(-11) GeV-1 for m(a) less than or similar to 4 x 10(-7) eV, depending on the assumptions on the magnetic fields and on the original gamma-ray spectrum. This new bound is complementary with other ALP constraints from very-high-energy gamma-ray experiments and sensitivities of future experiments.