Consider a fluid like water. Intuitively I would say that its viscosity is caused by intermolecular interactions among its molecules. But the Einstein-Smoluchowski relation (and the Fluctuation-Dissipation Theorem in general) says that viscosity is caused by the erratic motion of fluid particles. What I'm missing?
I think that the origin of viscosity is easy to understand with a help from analogy.
Imagine multiple parallel rail tracks. Trains consisting of flatbed wagons are moving along the same direction on all tracks but with slightly varying velocities. Workers standing on wagons are throwing sacks of sand in random directions onto nearby trains.
If we assume that in the reference frame of a given train the distribution of thrown sacks' momentum is isotropic it would not be so in the frame of another train. For example, sacks thrown from the fastest train would carry on average more momentum in the direction of motion than sacks thrown onto it and so this train would be slowing down while neighboring trains would be speeding up. We have a mechanism of diffusion for a momentum component along the direction of the tracks.
By formalising this analogy I believe it is possible to derive Einstein–Smoluchowski relation (at least up to a constant multiplier). So while indeed intermolecular interactions among (the fluid) molecules is an immediate mechanism for momentum exchange, the kinetic theory origin of viscosity is random motion of molecules that causes diffusion of net average of momentum.
From what I've found in textbooks, SE, and Wikipedia the viscosity theorization could be addressed considering (at least) two momentum transfer principles. The kinetic model based on brownian motion is dominant in gases, whereas for liquids the intermolecular forces play a major role.