  We explore the $511$~keV emission associated to sub-GeV dark matter (DM)
particles that can produce electron-positron pairs and form positronium after
thermalizing. We use $\sim16$~yr of SPI data from INTEGRAL to constrain DM
properties, considering the full positron propagation and losses, and the free
electron density drop away from the Galactic plane. We show that the predicted
longitude and latitude profiles vary significantly for different DM masses,
unlike previous assumptions, and obtain the strongest limits on sub-GeV DM
(from the MeV to a few GeV) so far, excluding cross-sections down to $\langle
\sigma v \rangle \lesssim10^{-32}$ cm$^3$ s$^{-1}$ for
$m_{\chi}\sim1\,\text{MeV}$ and $\langle \sigma v \rangle \lesssim10^{-26}$
cm$^3$ s$^{-1} $ for $m_{\chi}\sim5\,\text{GeV}$ and lifetimes up to $\tau
\gtrsim 10^{29}\, \textrm{s} \, (m_{\chi}\sim1\,\text{MeV}) $ and $\tau \gtrsim
10^{27}\,\textrm{s}$ ($m_{\chi}\sim5$~GeV) for the typical Navarro-Frenk-White
DM profile. Our derived limits are robust within a factor of a few due to
systematic uncertainties.
