The goal of this paper is propose a mathematical framework for optical flow refinement with non-quadratic regularization using variational techniques. We demonstrate how the model can be suitably adapted for both rigid and fluid motion estimation. We study the problem as an abstract IVP using an evolutionary PDE approach. We show that for a particular choice of constraint our model approximates the continuity model with non-quadratic regularization using augmented Lagrangian techniques. We subsequently show the results of our algorithm on different datasets.