The recent observation of NGC 1068 by the IceCube Neutrino Observatory has opened a new window to neutrino physics with astrophysical baselines. In this contribution, we show the results of a new method to probe the nature of neutrino masses using these observations. In particular, our method enables searching for signatures of pseudo-Dirac neutrinos with mass-squared differences that reach down to $\delta m^2 \geq 1e-21 \text{eV}^2$, improving the reach of terrestrial experiments by more than a billion. Finally, we discuss how the discovery of a constellation of neutrino sources can further increase the sensitivity and cover a wider range of $\delta m^2$ values.