The electron positron annihilation source in the Galactic center region has recently been observed with INTEGRAL/SPI, which shows that this 511 keV source is strong and its extension is consistent with the Galactic bulge geometry. The positron production rate, estimated to more than 1043 per second, is very high and raises a challenging question about the nature of the Galactic positron source. Commonly considered astrophysical positron injectors, namely type Ia supernovae are rare events and fall short to explain the observed positron production rate. In this paper, we study the possibility of Galactic positron production by hypernovae events, exemplified by the recently observed SN2003dh/GRB030329, an asymmetric explosion of a Wolf-Rayet star associated with a ?-ray burst. In these kinds of events, the ejected material becomes quickly transparent to positrons, which spread out in the interstellar medium. Non-radioactive processes, such as decays of heavy dark matter particles (neutralinos) predicted by most extensions of the standard model of particle physics, could also produce positrons as byproducts. However, they are expected to be accompanied by a large flux of high-energy ?-rays, which were not observed by EGRET and ground-based Tcherenkov experiments. In this context, we explore the possibility of direct positron production by annihilation of light dark matter particles.