  We describe the approach to lattice extraction of Generalized Parton
Distributions (GPDs) that is based on the use of the double distributions (DDs)
formalism within the pseudo-distribution framework. The advantage of using DDs
is that GPDs obtained in this way have the mandatory polynomiality property, a
non-trivial correlation between $x$- and $\xi$-dependences of GPDs. Another
advantage of using DDs is that the $D$-term appears as an independent entity in
the DD formalism rather than a part of GPDs $H$ and $E$. We relate the
$\xi$-dependence of GPDs to the width of the $\alpha$-profiles of the
corresponding DDs, and discuss strategies for fitting lattice-extracted
pseudo-distributions by DDs.
