  We investigate the spin transport across the magnetic phase diagram of a
frustrated antiferromagnetic insulator and uncover a drastic modification of
the transport regime from spin diffusion to spin superfluidity. Adopting a
triangular lattice accounting for both nearest neighbor and next-nearest
neighbor exchange interactions with easy-plane anisotropy, we perform atomistic
spin simulations on a two-terminal configuration across the full magnetic phase
diagram. We found that as long as the ground state magnetic moments remain
in-plane, irrespective of whether the magnetic configuration is ferromagnetic,
collinear or non-collinear antiferromagnetic, the system exhibits spin
superfluid behavior with a device output that is independent on the value of
the exchange interactions. When the magnetic frustration is large enough to
compete with the easy-plane anisotropy and cant the magnetic moments out of the
plane, the spin transport progressively evolves towards the diffusive regime.
The robustness of spin superfluidity close to magnetic phase boundaries is
investigated and we uncover the possibility for {\em proximate} spin
superfluidity close to the ferromagnetic transition.
