  Reconstructing dynamic 3D scenes from 2D images and generating diverse views
over time presents a significant challenge due to the inherent complexity and
temporal dynamics involved. While recent advancements in neural implicit models
and dynamic Gaussian Splatting have shown promise, limitations persist,
particularly in accurately capturing the underlying geometry of highly dynamic
scenes. Some approaches address this by incorporating strong semantic and
geometric priors through diffusion models. However, we explore a different
avenue by investigating the potential of regularizing the native warp field
within the dynamic Gaussian Splatting framework. Our method is grounded on the
key intuition that an accurate warp field should produce continuous space-time
motions. While enforcing the motion constraints on warp fields is non-trivial,
we show that we can exploit knowledge innate to the forward warp field network
to derive an analytical velocity field, then time integrate for scene flows to
effectively constrain both the 2D motion and 3D positions of the Gaussians.
This derived Lucas-Kanade style analytical regularization enables our method to
achieve superior performance in reconstructing highly dynamic scenes, even
under minimal camera movement, extending the boundaries of what existing
dynamic Gaussian Splatting frameworks can achieve.
