Here we show that coherent random walk in a perfectly periodic chain of dissipatively coupled bosonic modes can exhibit a variety of different anomalous transfer regimes in dependence on the initial state of the chain. In particular, for any given finite initial time-interval there is a set of initial states leading to hyper-ballistic transport regime. Also, there are initial states allowing to achieve a sub-diffusive regime or even localization for a given time-interval, or change asymptotic long-time diffusion rate. We show how these anomalous transport regimes can be practically realized in a planar system of coupled single-mode waveguides with designed loss.