We use the functional Renormalisation Group (fRG) to describe the in and out of equilibrium dynamics of stochastic processes, governed by an overdamped Langevin equation. Exploiting the connection between Langevin dynamics and supersymmetric quantum mechanics in imaginary time, we write down renormalisation group flow equations for the effective action, approximated in terms of the Local Potential Approximation and Wavefunction Renormalisation. We derive effective equations of motion (EEOM), from the effective action (EA) , for the average position, variance, and covariance. We also show how the fRG can offer strong agreement with direct numerical simulation of the nonequilibrium evolution of average position and variance in a fraction of the computation time hence effectively accelerating the dynamics. The fRG also offers other significant advantages over more standard techniques as when it is solved once it is essentially solved for all initial conditions. This is not so for direct numerical simulation and solving the Fokker-Planck diffusion equation meaning the computation gains are even greater when considering an ensemble of initial conditions.