π^3: Scalable Permutation-Equivariant Visual Geometry Learning

Yifan Wang, Zhou, Haoyi Zhu, Wenzheng Chang, Yang Zhou, Zizun Li, Junyi Chen, Jiangmiao Pang, Chunhua Shen, Tong He

π^3: Scalable Permutation-Equivariant Visual Geometry Learning: 67 upvotes on Hugging Face Daily Papers, #3 of 16 papers on 2025-07-18. Day-by-day upvote history.

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.

Paper page on Hugging Face · arXiv

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