  Gamma-ray bursts (GRBs) have been invoked to explain both the 511 keV
emission from the galactic bulge and the high-energy positron excess inferred
from the ATIC, PAMELA, and Fermi data. While independent explanations can be
responsible for these phenomena, we explore the possibility of their common
GRB-related origin by modeling the GRB distribution and estimating the rates.
For an expected Milky Way long GRB rate, neither of the two signals is generic;
the local excess requires a 2% coincidence, while the signal from the galactic
center requires a 20% coincidence with respect to the timing of the latest GRB.
The simultaneous explanation requires a 0.4% coincidence. Considering the large
number of statistical "trials" created by multiple searches for new physics,
the coincidences of a few per cent cannot be dismissed as unlikely.
Alternatively, both phenomena can be explained by GRBs if the galactic rate is
higher than expected. We also show that a similar result is difficult to obtain
assuming a simplified short GRB distribution.
