NSFlow: End-to-End Differentiable Neuro-Symbolic Optical Flow for Visual Odometry

Deep learning-based visual odometry (VO) has achieved significant progress, yet most existing methods focus on a monocular approach, which suffers from scale ambiguity. Stereo VO provides real metric by its nature, but remains less studied in deep learning VO due to its high computational cost and modeling complexity. Recent advances in stereo matching and optical flow estimation have made dense visual correspondence increasingly accurate and reliable, but their complementary geometric information has not been fully exploited for VO. In this paper, we present SFVO, a correspondence-driven stereo VO framework that directly builds upon pretrained stereo matching and optical flow models. SFVO exploits pretrained stereo matching and optical flow models to estimate stereo and temporal correspondences. Instead of learning pose directly from images, SFVO maps learned correspondences into geometric constraints and predicts which points are trustworthy. To improve the reliability of visual correspondence-based geometric constraints, we introduce decoupled confidence maps for rotation and translation. This design better aligns the characteristics of visual correspondence and 6-DoF transformations. Extensive experiments on outdoor and indoor datasets demonstrate that SFVO achieves robust and accurate pose estimation with strong generalization capability. The code will be released.

Dense visual odometry (VO), which provides pose estimation and dense 3D reconstruction, serves as the cornerstone for applications ranging from robotics to augmented reality. Recently, feed-forward models have demonstrated remarkable capabilities in dense mapping. However, when these models are used in dense visual SLAM systems, their heavy computational burden restricts them to yielding sparse pose outputs at keyframes while still failing to achieve real-time pose estimation. In contrast, traditional sparse methods provide high computational efficiency and high-frequency pose outputs, but lack the capability for dense reconstruction. To address these limitations, we propose HyVGGT-VO, a novel framework that combines the computational efficiency of sparse VO with the dense reconstruction capabilities of feed-forward models. To the best of our knowledge, this is the first work to tightly couple a traditional VO framework with VGGT, a state-of-the-art feed-forward model. Specifically, we design an adaptive hybrid tracking frontend that dynamically switches between traditional optical flow and the VGGT tracking head to ensure robustness. Furthermore, we introduce a hierarchical optimization framework that jointly refines VO poses and the scale of VGGT predictions to ensure global scale consistency. Our approach achieves an approximately 5x processing speedup compared to existing VGGT-based methods, while reducing the average trajectory error by 85% on the indoor EuRoC dataset and 12% on the outdoor KITTI benchmark. Our code will be publicly available upon acceptance. Project page: https://geneta2580.github.io/HyVGGT-VO.io.

Optical flow estimation is a fundamental problem in computer vision, yet the reliance on expensive ground-truth annotations limits the scalability of supervised approaches. Although unsupervised and semi-supervised methods alleviate this issue, they often suffer from unreliable supervision signals based on brightness constancy and smoothness assumptions, leading to inaccurate motion estimation in complex real-world scenarios. To overcome these limitations, we introduce \modelname, a novel framework that synthesizes large-scale, perfectly aligned frame--flow data pairs for supervised optical flow training without human annotations. Specifically, our method leverages a pre-trained depth estimation network to generate pseudo optical flows, which serve as conditioning inputs for a next-frame generation model trained to produce high-fidelity, pixel-aligned subsequent frames. This process enables the creation of abundant, high-quality synthetic data with precise motion correspondence. Furthermore, we propose an inconsistent pixel filtering strategy that identifies and removes unreliable pixels in generated frames, effectively enhancing fine-tuning performance on real-world datasets. Extensive experiments on KITTI2012, KITTI2015, and Sintel demonstrate that \modelname achieves competitive or superior results compared to existing unsupervised and semi-supervised approaches, highlighting its potential as a scalable and annotation-free solution for optical flow learning. We will release our code upon acceptance.