π^3: Scalable Permutation-Equivariant Visual Geometry Learning
Authors: name: Yifan Wang, name: Jianjun Zhou, name: Haoyi Zhu, name: Wenzheng Chang, name: Yang Zhou, name: Zizun Li, name: Junyi Chen, name: Jiangmiao Pang, name: Chunhua Shen, name: Tong He

We introduce pi^3, a feed-forward neural network that offers a novel
approach to visual geometry reconstruction, breaking the reliance on a
conventional fixed reference view. Previous methods often anchor their
reconstructions to a designated viewpoint, an inductive bias that can lead to
instability and failures if the reference is suboptimal. In contrast, pi^3
employs a fully permutation-equivariant architecture to predict
affine-invariant camera poses and scale-invariant local point maps without any
reference frames. This design makes our model inherently robust to input
ordering and highly scalable. These advantages enable our simple and bias-free
approach to achieve state-of-the-art performance on a wide range of tasks,
including camera pose estimation, monocular/video depth estimation, and dense
point map reconstruction. Code and models are publicly available.