The Jump Flooding Algorithm (JFA) as used here for calculating the distance transform is fairly quick and produces good, but not exact, results. But there also exist algorithms that produce the exact Euclidean Distance Transform (EDT) in linear time, such as described in A General Algorithm for Computing Distance Transforms in Linear Time (A. Meijster, J.B.T.M. Roerdink, W.H. Hesselink, A general algorithm for computing distance transforms in linear time, Computational Imaging and Vision 18 (8) (2000) 331–340) and A Linear Time Algorithm for Computing Exact Euclidean Distance Transforms of Binary Images in Arbitrary Dimensions (C.R. Maurer, R. Qi, and V. Raghavan, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(2):265–270, February 2003). This is straightforward to parallelise on CPUs, and has been implemented on GPUs (in Cuda) as well as the Parallel Banding Algorithm (Thanh-Tung Cao, Ke Tang, Anis Mohamed, and Tiow-Seng Tan, Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games (I3D '10)).

Would some of this be applicable here and possible to adapt to generate the anti-aliased distance transform? An exact algorithm would avoid the (small) errors still present in what Jump-Flooding calculates, and a linear-time algorithm might be able to calculate them a little bit more quickly as well; and a GPU implementation would seem to fit in well to be able to generate them from rendered content in real time within a game.