  We study branching diffusions in a bounded domain $D$ of $\mathbb{R}^d$ in
which particles are killed upon hitting the boundary $\partial D$. It is known
that any such process undergoes a phase transition when the branching rate
$\beta$ exceeds a critical value: a multiple of the first eigenvalue of the
generator of the diffusion. We investigate the system at criticality and show
that the associated genealogical tree, when the process is conditioned to
survive for a long time, converges to Aldous' Continuum Random Tree under
appropriate rescaling. The result holds under only a mild assumption on the
domain, and is valid for all branching mechanisms with finite variance, and a
general class of diffusions.
