  Models of spontaneous wave function collapse have been postulated to address
the measurement problem in quantum mechanics. Their primary function is to
convert coherent quantum superpositions into incoherent ones, with the result
that macroscopic objects cannot be placed into widely separated superpositions
for observably prolonged times. Many of these processes will also lead to loss
of coherence in neutrino oscillations, producing observable signatures in the
flavor profile of neutrinos at long travel distances. The majority of studies
of neutrino oscillation coherence to date have focused on variants of the
continuous state localization model, whereby an effective decoherence strength
parameter is used to model the rate of coherence loss with an assumed energy
dependence. Another class of collapse models that have been proposed posit
connections to the configuration of gravitational field accompanying the mass
distribution associated with each wave function that is in the superposition. A
particularly interesting and prescriptive model is Penrose's description of
gravitational collapse which proposes a decoherence time $\tau$ determined
through $E_{g}\tau\sim\hbar$, where $E_{g}$ is a calculable function of the
Newtonian gravitational potential. Here we explore application of the Penrose
collapse model to neutrino oscillations, reinterpreting previous experimental
limits on neutrino decoherence in terms of this model. We identify effects
associated with both spatial collapse and momentum diffusion, finding that the
latter is ruled out in data from the IceCube South Pole Neutrino Observatory so
long as the neutrino wave packet width at production is
$\sigma_{\nu,x}\leq2\times10^{-12}$ m.
