Spin transport via magnon diffusion in magnetic insulators is important for a broad range of spin-based phenomena and devices. However, the absence of the magnon equivalent of an electric force is a bottleneck. In this work, we demonstrate the controlled generation of magnon drift currents in yttrium iron garnet/platinum heterostructures. By performing electrical injection and detection of incoherent magnons, we find magnon drift currents that stem from the interfacial Dzyaloshinskii-Moriya interaction. We can further control the magnon drift by the orientation of the magnetic field. The drift current changes the magnon propagation length by up to $pm$ 6 % relative to diffusion. We generalize the magnonic spin transport theory to include a finite drift velocity resulting from any inversion asymmetric interaction, and obtain results consistent with our experiments.
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