  One of the main challenges in autonomous racing is to design algorithms for
motion planning at high speed, and across complex racing courses. End-to-end
trajectory synthesis has been previously proposed where the trajectory for the
ego vehicle is computed based on camera images from the racecar. This is done
in a supervised learning setting using behavioral cloning techniques. In this
paper, we address the limitations of behavioral cloning methods for trajectory
synthesis by introducing Differential Bayesian Filtering (DBF), which uses
probabilistic B\'ezier curves as a basis for inferring optimal autonomous
racing trajectories based on Bayesian inference. We introduce a trajectory
sampling mechanism and combine it with a filtering process which is able to
push the car to its physical driving limits. The performance of DBF is
evaluated on the DeepRacing Formula One simulation environment and compared
with several other trajectory synthesis approaches as well as human driving
performance. DBF achieves the fastest lap time, and the fastest speed, by
pushing the racecar closer to its limits of control while always remaining
inside track bounds.
