  The accretion of material from protoplanetary disks onto their central stars
is a fundamental process in the evolution of these systems and a key diagnostic
in constraining the disk lifetime. We analyze the relationship between the
stellar accretion rate and the disk mass in 32 intermediate-mass Herbig Ae/Be
systems and compare them to their lower-mass counterparts, T Tauri stars. We
find that the $\dot{M}$--$M_{\rm{disk}}$ relationship for Herbig Ae/Be stars is
largely flat at $\sim$10$^{-7}$ M$_{\odot}$ yr$^{-1}$ across over three orders
of magnitude in dust mass. While most of the sample follows the T Tauri trend,
a subset of objects with high accretion rates and low dust masses are
identified. These outliers (12 out of 32 sources) have an inferred disk
lifetime of less than 0.01 Myr and are dominated by objects with low infrared
excess. This outlier sample is likely identified in part by the bias in
classifying Herbig Ae/Be stars, which requires evidence of accretion that can
only be reliably measured above a rate of $\sim$10$^{-9}$ M$_{\odot}$ yr$^{-1}$
for these spectral types. If the disk masses are not underestimated and the
accretion rates are not overestimated, this implies that these disks may be on
the verge of dispersal, which may be due to efficient radial drift of material
or outer disk depletion by photoevaporation and/or truncation by companions.
This outlier sample likely represents a small subset of the larger young,
intermediate-mass stellar population, the majority of which would have already
stopped accreting and cleared their disks.
