  In this note we explore the structure of the diffusion metric of
Coifman-Lafon determined by fractional dyadic Laplacians. The main result is
that, for each ${t>0}$, the diffusion metric is a function of the dyadic
distance, given in $\mathbb{R}^+$ by $\delta(x,y) = \inf\{|I|: I \text{ is a
dyadic interval containing } x \text{ and } y\}$. Even if these functions of
$\delta$ are not equivalent to $\delta$, the families of balls are the same, to
wit, the dyadic intervals.
