We study the damping of perpendicular standing spin-waves (PSSWs) in ultrathin Fe films at frequencies up to 2.4 THz. The PSSWs are excited by optically generated ultrashort spin current pulses, and probed optically in the time domain. Analyzing the wavenumber and thickness dependence of the damping, we separate different contributions and demonstrate that at sufficiently large wave vectors $k$ the damping is dominated by spin transport effects scaling with k^4 and limiting the frequency range of observable PSSWs. Although such contribution is known to originate in the spin diffusion, we argue that at moderate and large k the super-diffusive character of the spin transport again reduces the related damping term.
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