  We study charge diffusion in holographic scaling theories with a
particle-hole symmetry. We show that these theories have a universal regime in
which the diffusion constant is given by $D_c = C v_B^2/ (2 \pi T)$ where $v_B$
is the velocity of the butterfly effect. The constant of proportionality, $C$,
depends only on the scaling exponents of the infra-red theory. Our results
suggest an unexpected connection between transport at strong coupling and
quantum chaos.
