$\pi^3$: Permutation-Equivariant Visual Geometry Learning

ICLR 2026 Conference Submission7040 Authors

Keywords: Permutation-Equivariance, 3D reconstruction, Reference-Free, Camera Pose Estimation, Depth Estimation

TL;DR: $\pi^3$ is a feed-forward model that reconstructs 3D geometry without a fixed reference view, making it more robust and accurate for tasks like camera pose and depth estimation.

Abstract: 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 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 will be publicly available.

Primary Area: applications to computer vision, audio, language, and other modalities

Submission Number: 7040