We introduce π3, 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, π3 employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. This design not only makes our model inherently robust to input ordering, but also leads to higher accuracy and performance. 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 available at https://github.com/yyfz/Pi3.
@article{arxiv.2507.13347,
title = {$\pi^3$: Permutation-Equivariant Visual Geometry Learning},
author = {Yifan Wang and Jianjun Zhou and Haoyi Zhu and Wenzheng Chang and Yang Zhou and Zizun Li and Junyi Chen and Jiangmiao Pang and Chunhua Shen and Tong He},
journal= {arXiv preprint arXiv:2507.13347},
year = {2026}
}