I will discuss the leading non-linear corrections to the Brownian motion of a heavy quark moving through a strongly coupled CFT plasma (bath) using holographic Schwinger-Keldysh path integral. The bulk spacetime in this formalism is a double copy of AdS black brane with a doubled string that probes it. The string stretches from two AdS boundaries and loops around a `horizon cap' connecting the horizons of the black branes. Evaluating the Nambu Goto action on this doubled string configuration results in the (quartic) influence phase of the heavy quark. The influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys recently developed non-linear fluctuation dissipation relation that relates the non-Gaussianity of thermal noise to the thermal jitter in the damping constant of the Brownian particle.