  This paper introduces FlowMap, an end-to-end differentiable method that
solves for precise camera poses, camera intrinsics, and per-frame dense depth
of a video sequence. Our method performs per-video gradient-descent
minimization of a simple least-squares objective that compares the optical flow
induced by depth, intrinsics, and poses against correspondences obtained via
off-the-shelf optical flow and point tracking. Alongside the use of point
tracks to encourage long-term geometric consistency, we introduce
differentiable re-parameterizations of depth, intrinsics, and pose that are
amenable to first-order optimization. We empirically show that camera
parameters and dense depth recovered by our method enable photo-realistic novel
view synthesis on 360-degree trajectories using Gaussian Splatting. Our method
not only far outperforms prior gradient-descent based bundle adjustment
methods, but surprisingly performs on par with COLMAP, the state-of-the-art SfM
method, on the downstream task of 360-degree novel view synthesis (even though
our method is purely gradient-descent based, fully differentiable, and presents
a complete departure from conventional SfM).
