The Galactic diffuse soft gamma-ray (30-800 keV) emission has been measured
from the Galactic center by the High Resolution Gamma-Ray and Hard X-Ray S
pectrometer balloon-borne germanium instrument to determine the spectral ch
aracteristics and origin of the emission. The resulting Galactic diffuse co
ntinuum is found to agree well with a single power law (plus positronium) o
ver the entire energy range, consistent with RXTE and COMPTEL/Compton Gamma
Ray Observatory observations at lower and higher energies, respectively. W
e find no evidence of spectral steepening below 200 keV, as has been report
ed in previous observations. The spatial distribution along the Galactic ri
dge is found to be nearly flat, with upper limits set on the longitudinal g
radient and with no evidence of an edge in the observed region. The soft ga
mma-ray diffuse spectrum is well modeled by inverse Compton scattering of i
nterstellar radiation off of cosmic-ray electrons, minimizing the need to i
nvoke inefficient nonthermal bremsstrahlung emission. The resulting power r
equirement is well within that provided by Galactic supernovae. We speculat
e that the measured spectrum provides the first direct constraints on the c
osmic-ray electron spectrum below 300 MeV.