  Quantum walks are known to propagate quadratically faster than their
classical counterparts and are used to model dynamics in various quantum
systems. The spread of the quantum walk in position space shows anomalous
diffusion behavior. By controlling the action of quantum coin operation on the
corresponding coin degree of freedom of the walker, one can demonstrate control
over the diffusion behavior. In this work, we report different forms of coin
operations on quantum walks exhibiting anomalous diffusion behavior.
Homogeneous and accelerated quantum walks display superdiffusive behavior,
whereas uncorrelated static and dynamic disorders in the evolution induce
strong and weak localization of the particle indicating subdiffusive and normal
diffusive behavior. The role played by the interference effects in the
spreading of the walker has remained elusive and our aim in this work is to
present the interplay between quantum coherence and mean squared displacement
of the walker. We employ two reliable measures of coherence for conclusively
establishing the role of quantum interference as the driving force behind the
anomalous diffusive behavior in the dynamics of quantum walks.
