  Using a high-resolution cosmological hydrodynamic simulation, we present a
method to constrain extinction due to intergalactic grey dust based on the
observed magnitudes of distant Type IA supernovae. We apply several simple
prescriptions to relate the intergalactic dust density to the gas density in
the simulation, thereby obtaining dust extinctions that may be directly
compared to the observed distribution of supernova magnitudes. Our analysis is
sensitive to the spatial distribution of grey dust, but is not dependent on its
intrinsic properties such as its opacity or grain size. We present an
application of our technique to the supernova data of Perlmutter et al., who
find that their high redshift sample is ~0.2 magnitudes fainter than the
expectation for a non-accelerating, low-density universe. We find that for grey
dust to be responsible, it must be distributed quite smoothly, e.g., tracing
intergalactic gas. More realistic dust distributions, such as dust tracing the
metal density, are inconsistent with observations at the 1.5-2 sigma level.
Upcoming observations and improved modelling of the dust distribution should
lead to stronger constraints on intergalactic grey dust extinction.
