# ProbFlow: Joint Optical Flow and Uncertainty Estimation

arXiv: https://arxiv.org/abs/1708.06509 · HTML: https://mlsanity.com/paper/1708.06509/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2017.

## Built on by (most cited first, 24 of 24)

- [SEA-RAFT: Simple, Efficient, Accurate RAFT for Optical Flow](https://mlsanity.com/paper/2405.14793/) (2024)
- [Learning Accurate Dense Correspondences and When to Trust Them](https://mlsanity.com/paper/2101.01710/) (2021)
- [PDC-Net+: Enhanced Probabilistic Dense Correspondence Network](https://mlsanity.com/paper/2109.13912/) (2021)
- [MFT: Long-Term Tracking of Every Pixel](https://mlsanity.com/paper/2305.12998/) (2023)
- [A survey on deep learning in medical image registration: new technologies, uncertainty, evaluation metrics, and beyond](https://mlsanity.com/paper/2307.15615/) (2023)
- [Probabilistic Warp Consistency for Weakly-Supervised Semantic Correspondences](https://mlsanity.com/paper/2203.04279/) (2022)
- [Gradient-based Uncertainty for Monocular Depth Estimation](https://mlsanity.com/paper/2208.02005/) (2022)
- [Diffusion Model for Dense Matching](https://mlsanity.com/paper/2305.19094/) (2023)
- [MAC-VO: Metrics-aware Covariance for Learning-based Stereo Visual Odometry](https://mlsanity.com/paper/2409.09479/) (2024)
- [URCDC-Depth: Uncertainty Rectified Cross-Distillation with CutFlip for Monocular Depth Estimation](https://mlsanity.com/paper/2302.08149/) (2023)
- [Uncertainty Quantification Metrics for Deep Regression](https://mlsanity.com/paper/2405.04278/) (2024)
- [DifFlow3D: Toward Robust Uncertainty-Aware Scene Flow Estimation with Diffusion Model](https://mlsanity.com/paper/2311.17456/) (2023)
- [Unsupervised confidence for LiDAR depth maps and applications](https://mlsanity.com/paper/2210.03118/) (2022)
- [PanMatch: Unleashing the Potential of Large Vision Models for Unified Matching Models](https://mlsanity.com/paper/2507.08400/) (2025)
- [On the calibration of underrepresented classes in LiDAR-based semantic segmentation](https://mlsanity.com/paper/2210.06811/) (2022)
- [Uncertainty Estimation in Deep Speech Enhancement Using Complex Gaussian Mixture Models](https://mlsanity.com/paper/2212.04831/) (2022)
- [Measuring and Modeling Uncertainty Degree for Monocular Depth Estimation](https://mlsanity.com/paper/2307.09929/) (2023)
- [MDMP: Multi-modal Diffusion for supervised Motion Predictions with uncertainty](https://mlsanity.com/paper/2410.03860/) (2024)
- [Chilled Sampling for Uncertainty Quantification: A Motivation From A Meteorological Inverse Problem](https://mlsanity.com/paper/2207.03182/) (2022)
- [Integrating Uncertainty into Neural Network-based Speech Enhancement](https://mlsanity.com/paper/2305.08744/) (2023)
- [A technique to jointly estimate depth and depth uncertainty for unmanned aerial vehicles](https://mlsanity.com/paper/2305.19780/) (2023)
- [UniFField: A Generalizable Unified Neural Feature Field for Visual, Semantic, and Spatial Uncertainties in Any Scene](https://mlsanity.com/paper/2510.06754/) (2025)
- [U2Flow: Uncertainty-Aware Unsupervised Optical Flow Estimation](https://mlsanity.com/paper/2604.10056/) (2026)
- [EECTracker: Swarm Motion Prior-Guided Feature Compensation for Airborne Optical UAV Swarm Tracking](https://mlsanity.com/paper/2609.15171/) (2026)

## Abstract (arXiv)

Optical flow estimation remains challenging due to untextured areas, motion boundaries, occlusions, and more. Thus, the estimated flow is not equally reliable across the image. To that end, post-hoc confidence measures have been introduced to assess the per-pixel reliability of the flow. We overcome the artificial separation of optical flow and confidence estimation by introducing a method that jointly predicts optical flow and its underlying uncertainty. Starting from common energy-based formulations, we rely on the corresponding posterior distribution of the flow given the images. We derive a variational inference scheme based on mean field, which incorporates best practices from energy minimization. An uncertainty measure is obtained along the flow at every pixel as the (marginal) entropy of the variational distribution. We demonstrate the flexibility of our probabilistic approach by applying it to two different energies and on two benchmarks. We not only obtain flow results that are competitive with the underlying energy minimization approach, but also a reliable uncertainty measure that significantly outperforms existing post-hoc approaches.