Arterial Spin Labelling is established as a quantitative technique to measure perfusion and other hemodynamic properties of the cerebral vasculature. This application of ASL requires multiple post label delays and parameter estimation via a kinetic model. However, the computational cost of the post-processing can be an issue, especially with sophisticated kinetic models. In this work, we propose a rapid method to perform perfusion estimation by replacing kinetic models with pre-trained neural networks. Two neural networks were trained to replace the kinetic model with or without gamma dispersion effects. The dispersion neural network is shown to achieve a lower computational cost.