  We introduce non-trivial contributions to diffusion constant in generic
many-body systems arising from quadratic fluctuations of ballistically
propagating, i.e. convective, modes. Our result is obtained by expanding the
current operator in the vicinity of equilibrium states in terms of powers of
local and quasi-local conserved quantities. We show that only the second-order
terms in this expansion carry a finite contribution to diffusive spreading. Our
formalism implies that whenever there are at least two coupled modes with
degenerate group velocities, the system behaves super-diffusively, in
accordance with the non-linear fluctuating hydrodynamics theory. Finally, we
show that our expression saturates the exact diffusion constants in quantum and
classical interacting integrable systems, providing a general framework to
derive these expressions.
