I study the diffuse flux of electron antineutrinos from stellar collapses with direct black hole formation (failed supernovae). This flux is more energetic than that from successful supernovae, and therefore it might contribute substantially to the total diffuse flux above realistic detection thresholds. The total flux might be considerably higher than previously thought, and approach the sensitivity of Super-Kamiokande. For more conservative values of the parameters, the flux from failed supernovae dominates for antineutrino energies above 30-45 MeV, with potential to give an observable spectral distortion at megaton detectors.