The positron emissivity of the Galactic bulge and disk, resulting from radioactivity of SNIa, is reassessed in the light of a recent evaluation of the SNIa rate. It is found that the disk may supply more positrons than required by recent SPI/INTEGRAL observations, but the bulge (where the characteristic positron annihilation line at 511 keV is in fact observed) only about 10%. It is argued that a large fraction of the disk positrons may be transported via the regular magnetic field of the Galaxy into the bulge, where they annihilate. This would increase both the bulge emissivity and the bulge/disk ratio, alleviating considerably the constraints imposed by INTEGRAL data analysis. We argue that the bulge/disk positron emissivity ratio can be considerably smaller than the values derived by the recent analysis of Knoedlseder et al. (2005), if the disk positrons diffuse sufficiently away from their sources, as required by our model; this possibility could be tested in the future, as data are accumulated in the SPI detectors. The success of the proposed scenario depends critically upon the, very poorly known at present, properties of the galactic magnetic field and of the propagation of low energy positrons in it.