  I show that by observing microlensing events both astrometrically and
photometrically, the Space Interferometry Mission (SIM) can measure the mass
function of stellar remnants in the Galactic bulge including white dwarfs,
neutron stars, and black holes. Neutron stars and black holes can be identified
individually, while white dwarfs are detected statistically from the sharp peak
in their mass function near M~ 0.6Msun. This peak is expected to be more than
twice as high as the `background' of main-sequence microlenses. I estimate that
of order 20% of the ~400 bulge microlensing events detected to date are due to
remnants, but show that these are completely unrecognizable from their time
scale distribution (the only observable that `normal' microlensing observations
produce). To resolve the white-dwarf peak, the SIM mass measurements must be
accurate to ~5%, substantially better than is required to measure the mass
function of the more smoothly distributed main sequence. Nevertheless, SIM
could measure the masses of about 20 bulge remnants in 500 hours of observing
time.
