  By applying the Covariant Entropy Bound (CEB) to an EFT in a box of size
$1/\Lambda_{\text{IR}}$ one obtains that the UV and IR cut-offs of the EFT are
necessarily correlated. We argue that in a theory of Quantum Gravity (QG) one
should identify the UV cutoff with the `species scale', and give a general
algorithm to calculate it in the case of multiple towers becoming light. One
then obtains an upper bound on the characteristic mass scale of the tower in
terms of the IR cut-off, given by $M_{\text{tower}}\lesssim
(\Lambda_{\text{IR}})^{2\alpha_D}$ in Planck units, with
$\alpha_D=(D-2+p)/2p(D-1)$, where $p$ depends on the density of states.
Identifying the IR cut-off with a (non-vanishing) curvature in AdS one
reproduces the statement of the AdS Distance Conjecture (ADC), also giving an
explicit lower bound for the $\alpha$ exponent. In particular, we find that the
CEB implies $\alpha \geq1/2$ in any dimension if there is a single KK tower,
both in AdS and dS vacua. However values $\alpha <1/2$ are allowed if the
particle tower is multiple or has a string component. We also consider the CKN
constraint coming from avoiding gravitational collapse which further requires
in general $\alpha \geq 1/D$ for the lightest tower. We analyse the case of the
DGKT-CFI class of Type IIA orientifold models and show it has both particle and
string towers below the species scale, so that a careful analysis of how the
ADC is defined is needed. We find that this class of models obey but do not
saturate the CEB. The UV/IR constraints found apply to both AdS and dS vacua.
We comment on possible applications of these ideas to the dS Swampland
conjecture as well as to the observed dS phase of the universe.
