  In the $m_Q\rightarrow\infty$ limit, the hyperfine splittings in the ground
state doubly heavy baryons $\left(QQq\right)$ and single heavy antimesons
$(\bar{Q}q)$ are related by heavy quark-diquark symmetry (HQDQ) as the light
degrees of freedom in both the hadrons are expected to have identical
configurations. In this article, working within the framework of
nonrelativistic QCD (NRQCD), we study the perturbative and nonperturbative
corrections to the HQDQ symmetry hyperfine splitting relation that scale as
${\cal O}\left(\alpha_s^2\right)$ and $\Lambda_{\rm QCD}^2/m_Q^2$ respectively.
In the extreme heavy quark limit, the perturbative corrections to hyperfine
splitting of doubly charm or bottom baryons are a few percent or smaller. The
nonperturbative corrections to hyperfine splitting are of order $10\%$ in the
case of doubly charm baryons and $1\%$ or smaller in doubly bottom baryons.
