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We study a minimal non-Markovian model of superdiffusion which originatesfrom long-range velocity correlations within the generalized Langevin equation(GLE) approach. The model allows for a three-dimensional Markovian embedding.The emergence of a transient hyperdiffusion, $< \Delta x^2(t)> \proptot^{2+\lambda}$, with $\lambda\sim 1-3$ is detected in tilted washboardpotentials before it ends up in a ballistic asymptotic regime. We relate thisphenomenon to a transient heating of particles $T_{\rm kin}(t)\proptot^\lambda$ from the thermal bath temperature $T$ to some maximal kinetictemperature $T_{\rm max}$. This hyperdiffusive transient regime ceases when theparticles arrive at the maximal kinetic temperature.

Origin of hyperdiffusion in generalized Brownian motion