  We analyze the 1496 days of SuperKamiokande data to put limits on the nue,
anti-nue, numu + nutau and anti-numu + anti-nutau components of the diffuse
flux of supernova neutrinos, in different energy intervals and for different
neutrino energy spectra. By considering the presence of only one component at a
time, we find the following bounds at 90% C.L. and for neutrino energy E>19.3$
MeV: Phi_{nue}<73.3-154 cm^-2 s^-1, Phi_{anti-nue} <1.4-1.9 cm^-2 s^-1,
Phi_{numu+nutau} <(1.0-1.4) 10^3 cm^-2 s^-1, and Phi_{anti-numu+ anti-nutau}
<(1.3-1.8) 10^3 cm^-2 s^-1, where the intervals account for varying the
neutrino spectrum. In the interval E = 22.9 - 36.9 MeV, we find Phi_{nue}<39-54
cm^-2 s^-1, which improves on the existing limit from SNO in the same energy
window. Our results for numu + nutau and anti-numu + anti-nutau improve by
about four orders of magnitude over the previous best constraints from LSD.
