  The three Standard Model neutrinos can have Majorana mass or strictly Dirac
mass, but both scenarios are practically indistinguishable in neutrino
oscillation experiments. If they are pseudo-Dirac, however, there will be new
mass splittings among the pseudo-Dirac pairs, potentially leaving traces in
neutrino oscillation phenomena. In this work, we use flavor ratios of
astrophysical neutrinos to discriminate different possible mass spectra of
pseudo-Dirac neutrinos. We show that it will be possible to impose robust
bounds of order $\delta m^2_3 \lesssim 10^{-12}$ $\text{eV}^2$ on the new mass
squared splitting involving the third pseudo-Dirac mass eigenstates (those with
the least electron flavor composition) with the future experiment IceCube-Gen2.
The derived sensitivity is robust because it only assumes an extragalactic
origin for the astrophysical neutrinos and hierarchical pseudo-Dirac mass
spectrum. In case the neutrino sources are known in the future, such bounds can
potentially improve by up to five orders of magnitude, reaching $\delta m^2_3
\lesssim 10^{-17}$ $\text{eV}^2$.
