The question how the visual system is able to create a coherent representation of a rapidly changing environment in the presence of neural delays is not fully resolved. In this paper we use an abstract probabilistic framework and a spiking neural network (SNN) implementation to investigate the role of motion-based prediction in estimating motion trajectories with delayed information sampling. In particular, we investigate how anisotropic diffusion of information may explain the development of anticipatory response in neural populations to an approaching stimulus. Inspired by a mechanism proposed by Nijhawan , we use a Bayesian particle filter framework and introduce a diagonal motion-based prediction model which extrapolates the estimated response to delayed stimulus in the direction of the trajectory. In the SNN implementation, we have used anisotropic recurrent connections between excitatory cells as mechanism for motion-extrapolation. Consistent with recent experimental data collected in extracellular recordings of macaque primary visual cortex [Benvenuti et al 2011], we have simulated different trajectory lengths and have explored how anticipatory response may be dependent to the information accumulated along the trajectory. We show that both our probabilistic framework and the SNN can replicate the experimental data qualitatively. Most importantly, we highlight requirements for the development of a trajectory-dependent anticipatory response, and in particular the anisotropic nature of the diagonal motion extrapolation mechanism.