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Manipulation of magnetic domain walls via a helicity-independent laser pulse has recently been experimentally demonstrated and various physical mechanisms leading to domain wall dynamics have been discussed. Spin-dependent superdiffusive transport of hot electrons has been identified as one of the possible ways to affect a magnetic domain wall. Here, we develop a model based on superdiffusive spin-dependent transport to study the laser-induced transport of hot electrons through a smooth magnetic domain wall. We show that the spin transfer between neighboring domains can enhance ultrafast demagnetization in the domain wall. More importantly, our calculations reveal that when the laser pulse is properly focused onto the vicinity of the domain wall, it can excite sufficiently strong spin currents to generate a spin-transfer torque that can rapidly move the magnetic domain wall by several nanometers in several hundred femtoseconds, leading to a huge nonequilibrium domain wall velocity.