  The interplay between disorder and quantum interference leads to a wide
variety of physical phenomena including celebrated Anderson localization -- the
complete absence of diffusive transport due to quantum interference between
different particle trajectories. In two dimensions, any amount of disorder is
thought to induce localization of all states at long enough length scales,
though this may be prevented if bands are topological or have strong spin-orbit
coupling. In this note, we present a simple argument providing another
mechanism for disrupting localization: by tuning the underlying curvature of
the manifold on which diffusion takes place. We show that negative curvature
manifolds contain a natural infrared cut off for the probability of self
returning paths. We provide explicit calculations of the Cooperon -- directly
related to the weak-localization corrections to the conductivity -- in
hyperbolic space. It is shown that constant negative curvature leads to a rapid
growth in the number of available trajectories a particle can coherently
traverse in a given time, reducing the importance of interference effects and
restoring classical diffusive behavior even in the absence of inelastic
collisions. We conclude by arguing that this result may be amenable to
experimental verification through the use of quantum simulators.
