mlsanityData to 7 Oct 2026

π3: Permutation-Equivariant Visual Geometry Learning

arXiv 2507.13347 ↗First posted 17 Jul 2025cs.CVcited by 292

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Abstract (arXiv)

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.

Key facts. Cited by 292 papers in the map (data through 7 Oct 2026). Builds on 38 of its 51 references that are in the map. First posted on arXiv 17 Jul 2025.

Builds on

38 of 51 references.

References · 38

  1. 2023DINOv2: Learning Robust Visual Features without Supervisioncited by 7,764
  2. 2017ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenescited by 3,088
  3. 2023DUSt3R: Geometric 3D Vision Made Easycited by 1,526
  4. 2025VGGT: Visual Geometry Grounded Transformercited by 1,475
  5. 2024Depth Anything V2cited by 1,385
  6. 2019Habitat: A Platform for Embodied AI Researchcited by 1,163
  7. 2015ORB-SLAM: a Versatile and Accurate Monocular SLAM Systemcited by 983
  8. 2024Grounding Image Matching in 3D with MASt3Rcited by 960
  9. 2023ScanNet++: A High-Fidelity Dataset of 3D Indoor Scenescited by 747
  10. 2018MegaDepth: Learning Single-View Depth Prediction from Internet Photoscited by 731
  11. 2021Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstructioncited by 646
  12. 2018Taskonomy: Disentangling Task Transfer Learningcited by 631
26 more
  1. 2020Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understandingcited by 593
  2. 2025Continuous 3D Perception Model with Persistent Statecited by 527
  3. 2020TartanAir: A Dataset to Push the Limits of Visual SLAMcited by 494
  4. 2019BlendedMVS: A Large-scale Dataset for Generalized Multi-view Stereo Networkscited by 487
  5. 2021ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Datacited by 442
  6. 2024MonST3R: A Simple Approach for Estimating Geometry in the Presence of Motioncited by 431
  7. 2025Fast3R: Towards 3D Reconstruction of 1000+ Images in One Forward Passcited by 356
  8. 2021Neural RGB-D Surface Reconstructioncited by 312
  9. 2024MoGe: Unlocking Accurate Monocular Geometry Estimation for Open-Domain Images with Optimal Training Supervisioncited by 290
  10. 20243D Reconstruction with Spatial Memorycited by 269
  11. 2025MoGe-2: Accurate Monocular Geometry with Metric Scale and Sharp Detailscited by 250
  12. 2024Global Structure-from-Motion Revisitedcited by 215
  13. 2023Project Aria: A New Tool for Egocentric Multi-Modal AI Researchcited by 201
  14. 2023MatrixCity: A Large-scale City Dataset for City-scale Neural Rendering and Beyondcited by 185
  15. 2019ReFusion: 3D Reconstruction in Dynamic Environments for RGB-D Cameras Exploiting Residualscited by 180
  16. 2025FLARE: Feed-forward Geometry, Appearance and Camera Estimation from Uncalibrated Sparse Viewscited by 176
  17. 2023PoseDiffusion: Solving Pose Estimation via Diffusion-aided Bundle Adjustmentcited by 146
  18. 2024MV-DUSt3R+: Single-Stage Scene Reconstruction from Sparse Views In 2 Secondscited by 136
  19. 2024RGBD Objects in the Wild: Scaling Real-World 3D Object Learning from RGB-D Videoscited by 113
  20. 2021TransformerFusion: Monocular RGB Scene Reconstruction using Transformerscited by 107
  21. 2025Aether: Geometric-Aware Unified World Modelingcited by 94
  22. 2022ParticleSfM: Exploiting Dense Point Trajectories for Localizing Moving Cameras in the Wildcited by 90
  23. 2020An Analysis of SVD for Deep Rotation Estimationcited by 85
  24. 2024Reloc3r: Large-Scale Training of Relative Camera Pose Regression for Generalizable, Fast, and Accurate Visual Localizationcited by 81
  25. 2024Point Cloud Matters: Rethinking the Impact of Different Observation Spaces on Robot Learningcited by 45
  26. 2019Flow-Motion and Depth Network for Monocular Stereo and Beyondcited by 37

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 25; 2026: 267.

292 papers.

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  1. 2025ViPE: Video Pose Engine for 3D Geometric Perceptioncited by 162
  2. 2025FastVGGT: Training-Free Acceleration of Visual Geometry Transformercited by 93
  3. 2026SANA-WM: Efficient Minute-Scale World Modeling with Hybrid Linear Diffusion Transformercited by 50
  4. 2025Efficiently Reconstructing Dynamic Scenes One D4RT at a Timecited by 46
  5. 2025G2VLM: Geometry Grounded Vision Language Model with Unified 3D Reconstruction and Spatial Reasoningcited by 39
  6. 2026LoGeR: Long-Context Geometric Reconstruction with Hybrid Memorycited by 33
  7. 2025WinT3R: Window-Based Streaming Reconstruction with Camera Token Poolcited by 32
  8. 2026LingBot-Map: Geometric Context Transformer for Streaming 3D Reconstructioncited by 32
  9. 2026V-DPM: 4D Video Reconstruction with Dynamic Point Mapscited by 29
  10. 2026WorldMark: A Unified Benchmark Suite for Interactive Video World Modelscited by 24
  11. 2025SpaceMind: Camera-Guided Modality Fusion for Spatial Reasoning in Vision-Language Modelscited by 21
  12. 2025Generative Video Motion Editing with 3D Point Trackscited by 21
38 more
  1. 2025DVGT: Driving Visual Geometry Transformercited by 20
  2. 2026VGGT-Omegacited by 20
  3. 2025Emergent Outlier View Rejection in Visual Geometry Grounded Transformerscited by 19
  4. 2025RealX3D: A Physically-Degraded 3D Benchmark for Multi-view Visual Restoration and Reconstructioncited by 19
  5. 2026VideoGPA: Distilling Geometry Priors for 3D-Consistent Video Generationcited by 19
  6. 2026INSPATIO-WORLD: A Real-Time 4D World Simulator via Spatiotemporal Autoregressive Modelingcited by 18
  7. 20264RC: 4D Reconstruction via Conditional Querying Anytime and Anywherecited by 17
  8. 2026LongStream: Long-Sequence Streaming Autoregressive Visual Geometrycited by 17
  9. 2026Vision-aligned Latent Reasoning for Multi-modal Large Language Modelcited by 16
  10. 2026Thinking with Geometry: Active Geometry Integration for Spatial Reasoningcited by 14
  11. 2026VGG-T3: Offline Feed-Forward 3D Reconstruction at Scalecited by 14
  12. 2025Reconstructing 4D Spatial Intelligence: A Surveycited by 13
  13. 2026SpatialClaw: Rethinking Action Interface for Agentic Spatial Reasoningcited by 13
  14. 2026CoWTracker: Tracking by Warping instead of Correlationcited by 12
  15. 2026Repurposing Geometric Foundation Models for Multi-view Diffusioncited by 12
  16. 2026DVGT-2: Vision-Geometry-Action Model for Autonomous Driving at Scalecited by 12
  17. 2026WAM4D: Fast 4D World Action Model via Spatial Register Tokenscited by 12
  18. 2026ROCKET: Residual-Oriented Multi-Layer Alignment for Spatially-Aware Vision-Language-Action Modelscited by 11
  19. 2026VGGT-World: Transforming VGGT into an Autoregressive Geometry World Modelcited by 11
  20. 2025Text-to-3D by Stitching a Multi-view Reconstruction Network to a Video Generatorcited by 10
  21. 2025GLaD: Geometric Latent Distillation for Vision-Language-Action Modelscited by 10
  22. 2025Learning to Reason in 4D: Dynamic Spatial Understanding for Vision Language Modelscited by 10
  23. 2026Track4World: Feedforward World-centric Dense 3D Tracking of All Pixelscited by 10
  24. 2026NavDreamer: Video Models as Zero-Shot 3D Navigatorscited by 9
  25. 2026ShareVerse: Multi-Agent Consistent Video Generation for Shared World Modelingcited by 9
  26. 20263D-Fixer: Coarse-to-Fine In-place Completion for 3D Scenes from a Single Imagecited by 9
  27. 2025Off The Grid: Detection of Primitives for Feed-Forward 3D Gaussian Splattingcited by 8
  28. 2026MVGGT: Multimodal Visual Geometry Grounded Transformer for Multiview 3D Referring Expression Segmentationcited by 8
  29. 2026MoRe: Motion-aware Feed-forward 4D Reconstruction Transformercited by 8
  30. 2026WorldRoamBench: An Open-World Benchmark for Long-Horizon Stability of Interactive World Modelscited by 8
  31. 2025Taming Camera-Controlled Video Generation with Verifiable Geometry Rewardcited by 7
  32. 2026EgoGrasp: World-Space Hand-Object Interaction Estimation from Egocentric Videoscited by 7
  33. 2026ShotVerse: Advancing Cinematic Camera Control for Text-Driven Multi-Shot Video Creationcited by 7
  34. 2026VGGT-Motion: Motion-Aware Calibration-Free Monocular SLAM for Long-Range Consistencycited by 6
  35. 2026Flow3r: Factored Flow Prediction for Scalable Visual Geometry Learningcited by 6
  36. 2026Spa3R: Predictive Spatial Field Modeling for 3D Visual Reasoningcited by 6
  37. 2026Allocentric Perceiver: Disentangling Allocentric Reasoning from Egocentric Visual Priors via Frame Instantiationcited by 5
  38. 2026Driving with DINO: Vision Foundation Features as a Unified Bridge for Sim-to-Real Generation in Autonomous Drivingcited by 5

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