Considering the following two phenomena:
Adiabatic quantum computing in general exhibits a quadratic speedup over classical simulated annealing, though for some Hamiltonians it may be faster (while for others slower). Typically, quantum tunneling is referred to as the reason for this speedup. (Mukherjee, S., Chakrabarti, B. Multivariable optimization: Quantum annealing and computation. Eur. Phys. J. Spec. Top. 224, 17–24 (2015). https://doi.org/10.1140/epjst/e2015-02339-y)
Quantum walks on graphs in general exhibit quadratic improved hit time over their classical counterparts, though for some nodes in some graphs this may be exponentially fast while for others it may be slower. In describing the reason behind this, authors usually refer not to tunneling but interference, pointing out that amplitudes on some graph nodes will constructively interfere while others will destructively interfere. (Kempe, J. Discrete Quantum Walks Hit Exponentially Faster. Probab. Theory Relat. Fields 133, 215–235 (2005). https://doi.org/10.1007/s00440-004-0423-2)
Are these separate phenomena, or are they two different statements of the same underlying result? I noticed (through my distinctly non-random sampling of a few papers on each) that quantum walk papers rarely mention adiabatic computation, and vice versa.