  In this article, we reevaluate supernovae (SN) constraints on the diffusion
time of neutrinos for a family of extensions of the Standard Model that
incorporate new light scalar and vector mediators. We compute the neutrino mean
free path, taking into account medium effects in the neutrino-nucleon
scattering cross-section, and a radial dependence of the density, energy, and
temperature inside the proto-neutron star to determine the coupling strengths
compatible with SN1987A constraints on the time duration signal of diffusing
neutrinos. We show that medium effects can induce an order of magnitude
enhancement in the neutrino mean free path with respect to the vacuum
calculation. The increase is more significant when new physics terms dominate
over the Standard Model contribution (that is, for small mediator mass and
large couplings). Finally, we interpret these results as bounds on the
parameter space of a vector $U(1)_{B-L}$ model and scalar lepton number
conserving and lepton number violating scenarios, improving on previous results
in the literature where medium effects were ignored. We show that SN
constraints on the neutrino diffusion time lie within regions of the parameter
space that are already ruled out by other experimental constraints. We also
comment on potential limits due to changes in the SN equation of state or
right-handed neutrino free-streaming, but argue that detailed numerical
simulations are needed to improve the reliability of these limits.
