  The distance conjecture diagnoses viable low-energy effective realisation of
consistent theories of quantum gravity by examining their breakdown at infinite
distance in their parameter space. At the same time, infinite distance points
in parameter space are naturally intertwined with string dualities. We explore
the implications of the distance conjecture when T-duality is applied to curved
compact manifolds and in presence of (non-)geometric fluxes. We provide
evidence of how divergent potentials signal pathological infinite distance
points in the scalar field space where towers of light states cannot be
sustained by the curved background. This leads us to suggest an extension to
the current statement of the Swampland distance conjecture in curved spaces or
in presence of non-trivial fluxes supporting the background.
