  Transport in strongly-disordered, metallic systems is governed by diffusive
processes. Based on quantum mechanics, it has been conjectured that these
diffusivities obey a lower bound $D/v^2\gtrsim \hbar/k_B T$, the saturation of
which provides a mechanism for the T-linear resistivity of bad metals. This
bound features a characteristic velocity $v$, which was later argued to be the
butterfly velocity $v_B$, based on holographic models of transport. This
establishes a link between incoherent metallic transport, quantum chaos and
Planckian timescales. Here we study higher derivative corrections to an
effective holographic action of homogeneous disorder. The higher derivative
terms involve only the charge and translation symmetry breaking sector. We show
that they have a strong impact on the bound on charge diffusion
$D_c/v_B^2\gtrsim \hbar/k_B T$, by potentially making the coefficient of its
right-hand side arbitrarily small. On the other hand, the bound on energy
diffusion is not affected.
