  In this paper we present a new method for deformable NeRF that can directly
use optical flow as supervision. We overcome the major challenge with respect
to the computationally inefficiency of enforcing the flow constraints to the
backward deformation field, used by deformable NeRFs. Specifically, we show
that inverting the backward deformation function is actually not needed for
computing scene flows between frames. This insight dramatically simplifies the
problem, as one is no longer constrained to deformation functions that can be
analytically inverted. Instead, thanks to the weak assumptions required by our
derivation based on the inverse function theorem, our approach can be extended
to a broad class of commonly used backward deformation field. We present
results on monocular novel view synthesis with rapid object motion, and
demonstrate significant improvements over baselines without flow supervision.
