  Generating smooth animations from a limited number of sequential observations
has a number of applications in vision. For example, it can be used to increase
number of frames per second, or generating a new trajectory only based on first
and last frames, e.g. a motion of face emotions. Despite the discrete observed
data (frames), the problem of generating a new trajectory is a continues
problem. In addition, to be perceptually realistic, the domain of an image
should not alter drastically through the trajectory of changes. In this paper,
we propose a new framework, Warping Neural ODE, for generating a smooth
animation (video frame interpolation) in a continuous manner, given two
("farther apart") frames, denoting the start and the end of the animation. The
key feature of our framework is utilizing the continuous spatial transformation
of the image based on the vector field, derived from a system of differential
equations. This allows us to achieve the smoothness and the realism of an
animation with infinitely small time steps between the frames. We show the
application of our work in generating an animation given two frames, in
different training settings, including Generative Adversarial Network (GAN) and
with $L_2$ loss.
