# QuacamFM: Quaternion-Constrained Flow Matching for Camera Pose Estimation

arXiv: https://arxiv.org/abs/2609.32455 · HTML: https://mlsanity.com/paper/2609.32455/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [VGGT: Visual Geometry Grounded Transformer](https://mlsanity.com/paper/2503.11651/) (2025)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [SynSin: End-to-end View Synthesis from a Single Image](https://mlsanity.com/paper/1912.08804/) (2019)
- [RoMa: Robust Dense Feature Matching](https://mlsanity.com/paper/2305.15404/) (2023)
- [Visual Geometry Grounded Deep Structure From Motion](https://mlsanity.com/paper/2312.04563/) (2023)
- [Image Matching across Wide Baselines: From Paper to Practice](https://mlsanity.com/paper/2003.01587/) (2020)
- [Pixel-Perfect Structure-from-Motion with Featuremetric Refinement](https://mlsanity.com/paper/2108.08291/) (2021)
- [FLARE: Feed-forward Geometry, Appearance and Camera Estimation from Uncalibrated Sparse Views](https://mlsanity.com/paper/2502.12138/) (2025)
- [MASt3R-SfM: a Fully-Integrated Solution for Unconstrained Structure-from-Motion](https://mlsanity.com/paper/2409.19152/) (2024)
- [Geometry-Aware Learning of Maps for Camera Localization](https://mlsanity.com/paper/1712.03342/) (2017)
- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [PoseDiffusion: Solving Pose Estimation via Diffusion-aided Bundle Adjustment](https://mlsanity.com/paper/2306.15667/) (2023)
- [Cameras as Rays: Pose Estimation via Ray Diffusion](https://mlsanity.com/paper/2402.14817/) (2024)
- [Learning Multi-Scene Absolute Pose Regression with Transformers](https://mlsanity.com/paper/2103.11468/) (2021)
- [RelPose: Predicting Probabilistic Relative Rotation for Single Objects in the Wild](https://mlsanity.com/paper/2208.05963/) (2022)
- [RelPose++: Recovering 6D Poses from Sparse-view Observations](https://mlsanity.com/paper/2305.04926/) (2023)
- [DeDoDe: Detect, Don't Describe -- Describe, Don't Detect for Local Feature Matching](https://mlsanity.com/paper/2308.08479/) (2023)

## Abstract (arXiv)

Camera pose estimation from multi-view images remains a challenge in computer vision. Traditional methods often address this problem using Structure-from-Motion (SfM) with bundle adjustment. However, camera poses estimated from sparse views are inherently ambiguous due to insufficient geometric constraints. Recent work leverages probabilistic models, such as diffusion models, to generate multiple camera pose hypotheses and therefore capture this uncertainty better. Most of these methods represent camera rotations using unit quaternions, but treat them as unconstrained 4D vectors during the generative processes, thereby ignoring the unit-norm constraint of quaternions. Unconstrained quaternions create non-smooth and suboptimal generation trajectories. To this end, we propose *QuacamFM*, a quaternion-constrained flow matching framework for camera pose estimation that preserves unit quaternion representations throughout the entire flow trajectory. We design the optimal transport of the quaternion flows using smooth spherical linear interpolation. Experiments on CO3Dv2 demonstrate our method's advantage in camera pose accuracy over diffusion-based methods and classical SfM approaches. We further show that our quaternion-constrained formulation outperforms the naive application of standard flow matching to 4D quaternion vectors on sparse-view camera pose estimation. Finally, it is observed that QuacamFM generalizes well across datasets and in-the-wild examples.