Molecular motors translocate along cytoskeletal filaments, as in the case of kinesin motors on microtubules. Although conventional kinesin-1 tracks a single microtubule protofilament, other kinesins, akin to dyneins, switch protofilaments. However, the molecular trajectory-whether protofilament switching occurs in a directed or stochastic manner-is unclear. Here, we used high-resolution optical tweezers to track the path of single budding yeast kinesin-8, Kip3, motor proteins. Under applied sideward loads, we found that individual motors stepped sideward in both directions, with and against loads, with a broad distribution in measured step sizes. Interestingly, the force response depended on the direction. Based on a statistical analysis and simulations accounting for the geometry, we propose a diffusive sideward stepping motion of Kip3 on the microtubule lattice, asymmetrically biased by force. This finding is consistent with previous multimotor gliding assays and sheds light on the molecular switching mechanism. For kinesin-8, the diffusive switching mechanism may enable the motor to bypass obstacles and reach the microtubule end for length regulation. For other motors, such a mechanism may have implications for torque generation around the filament axis.