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The typical transverse momentum Qs(t) (or "saturation" momentum) acquired by a hard particle propagating through a N = 4 SYM plasma increases over time like tγ, with an anomalous exponent γ > 1/2 characteristic of super-diffusion. This anomalous exponent is a function of the ’t Hooft coupling λ = g2Nc. Recently, a method has been proposed to systematically compute the perturbative series of γ(λ) at weak coupling. This method relies on the traveling wave interpretation of the time evolution of Qs(t) and on the dominance of softcollinear radiative corrections at large times. In this paper, we compute γ(λ) up to 𝒪(λ2) using the double logarithmic behaviour of the BFKL equation in planar 𝒩 = 4 SYM at three loops. This calculation allows us to discuss the transition towards the strong coupling regime where AdS/CFT calculations predict γ→1.