  Previous works have controversially claimed near-room temperature
ferromagnetism in two-dimensional (2D) VSe$_2$, with conflicting results
throughout the literature. These discrepancies in magnetic properties between
both phases (T and H phase) of 2D VSe$_2$ are most likely due to the structural
parameters being coupled to the magnetic properties. Specifically, both phases
have a close lattice match and similar total energies, which makes it difficult
to determine which phase is being observed experimentally. In this study, we
used a combination of density functional theory (DFT), highly accurate
diffusion Monte Carlo (DMC) and a surrogate Hessian line-search optimization
technique to resolve the previously reported discrepancy in structural
parameters and relative phase stability. With DMC accuracy, we determined the
freestanding geometry of both phases and constructed a phase diagram. Our
findings demonstrate the successes of the DMC method coupled with the surrogate
Hessian structural optimization technique when applied to a 2D magnetic system.
