  The information metric provides a unique notion of distance along any
continuous family of physical theories, placing two theories further apart the
more distinguishable they are. As such, the information metric is typically
singular at quantum critical points, reflecting the fact they make
qualitatively different scale-invariant predictions when compared to other
theories in the family. However, such singularities are always at finite
distance. The goal of this paper is to study infinite distance metric
singularities and understand what type of physics generates them. We argue that
infinite distance limits in the information metric correspond to theories in
which expectation values factorize, and that unitarity restricts the asymptotic
form of the metric to have a universal logarithmic singularity whose
coefficient only depends on how the factorization limit is approached. We
illustrate this relationship in a set of wide-ranging examples. Furthermore, we
argue that it provides a particularly simple bottom-up motivation for the
seemingly universal behavior of quantum gravity in asymptotic regions of moduli
space described by the Swampland Distance Conjecture: gravity universally
couples to stress-energy and thus abhors factorization limits. The towers of
light fields that appear in these limits in so many examples serve to decouple
gravity and consistently allow for factorization. We make this more precise via
holography and suggest a way to consistently realize infinite distance limits
without a tower of light fields.
