  Transport of strongly interacting fermions governs modern materials -- from
the high-$T_c$ cuprates to bilayer graphene --, but also nuclear fission, the
merging of neutron stars and the expansion of the early universe. Here we
observe a universal quantum limit of diffusivity in a homogeneous, strongly
interacting Fermi gas of atoms by studying sound propagation and its
attenuation via the coupled transport of momentum and heat. In the normal
state, the sound diffusivity ${D}$ monotonically decreases upon lowering the
temperature $T$, in contrast to the diverging behavior of weakly interacting
Fermi liquids. As the superfluid transition temperature is crossed, ${D}$
attains a universal value set by the ratio of Planck's constant ${h}$ and the
particle mass ${m}$. This finding of quantum limited sound diffusivity informs
theories of fermion transport, with relevance for hydrodynamic flow of
electrons, neutrons and quarks.
