  Much of computer-generated animation is created by manipulating meshes with
rigs. While this approach works well for animating articulated objects like
animals, it has limited flexibility for animating less structured free-form
objects. We introduce Wassersplines, a novel trajectory inference method for
animating unstructured densities based on recent advances in continuous
normalizing flows and optimal transport. The key idea is to train a
neurally-parameterized velocity field that represents the motion between
keyframes. Trajectories are then computed by advecting keyframes through the
velocity field. We solve an additional Wasserstein barycenter interpolation
problem to guarantee strict adherence to keyframes. Our tool can stylize
trajectories through a variety of PDE-based regularizers to create different
visual effects. We demonstrate our tool on various keyframe interpolation
problems to produce temporally-coherent animations without meshing or rigging.
