# Triangular Consistency as a Universal Constraint for Learning Optical Flow

arXiv: https://arxiv.org/abs/2606.19938 · HTML: https://mlsanity.com/paper/2606.19938/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 78 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 30 of 47)

- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [TAPIR: Tracking Any Point with per-frame Initialization and temporal Refinement](https://mlsanity.com/paper/2306.08637/) (2023)
- [FlowFormer: A Transformer Architecture for Optical Flow](https://mlsanity.com/paper/2203.16194/) (2022)
- [Learning Correspondence from the Cycle-Consistency of Time](https://mlsanity.com/paper/1903.07593/) (2019)
- [UnFlow: Unsupervised Learning of Optical Flow with a Bidirectional Census Loss](https://mlsanity.com/paper/1711.07837/) (2017)
- [Tracking Everything Everywhere All at Once](https://mlsanity.com/paper/2306.05422/) (2023)
- [SEA-RAFT: Simple, Efficient, Accurate RAFT for Optical Flow](https://mlsanity.com/paper/2405.14793/) (2024)
- [DF-Net: Unsupervised Joint Learning of Depth and Flow using Cross-Task Consistency](https://mlsanity.com/paper/1809.01649/) (2018)
- [SelFlow: Self-Supervised Learning of Optical Flow](https://mlsanity.com/paper/1904.09117/) (2019)
- [What Matters in Unsupervised Optical Flow](https://mlsanity.com/paper/2006.04902/) (2020)
- [Learning by Analogy: Reliable Supervision from Transformations for Unsupervised Optical Flow Estimation](https://mlsanity.com/paper/2003.13045/) (2020)
- [Back to Basics: Unsupervised Learning of Optical Flow via Brightness Constancy and Motion Smoothness](https://mlsanity.com/paper/1608.05842/) (2016)
- [Occlusion Aware Unsupervised Learning of Optical Flow](https://mlsanity.com/paper/1711.05890/) (2017)
- [Unsupervised Depth Completion from Visual Inertial Odometry](https://mlsanity.com/paper/1905.08616/) (2019)
- [CRAFT: Cross-Attentional Flow Transformer for Robust Optical Flow](https://mlsanity.com/paper/2203.16896/) (2022)
- [VideoFlow: Exploiting Temporal Cues for Multi-frame Optical Flow Estimation](https://mlsanity.com/paper/2303.08340/) (2023)
- [EpicFlow: Edge-Preserving Interpolation of Correspondences for Optical Flow](https://mlsanity.com/paper/1501.02565/) (2015)
- [SMURF: Self-Teaching Multi-Frame Unsupervised RAFT with Full-Image Warping](https://mlsanity.com/paper/2105.07014/) (2021)
- [DDFlow: Learning Optical Flow with Unlabeled Data Distillation](https://mlsanity.com/paper/1902.09145/) (2019)
- [MFT: Long-Term Tracking of Every Pixel](https://mlsanity.com/paper/2305.12998/) (2023)
- [Unsupervised Depth Completion with Calibrated Backprojection Layers](https://mlsanity.com/paper/2108.10531/) (2021)
- [Dense Optical Tracking: Connecting the Dots](https://mlsanity.com/paper/2312.00786/) (2023)
- [SKFlow: Learning Optical Flow with Super Kernels](https://mlsanity.com/paper/2205.14623/) (2022)
- [MemFlow: Optical Flow Estimation and Prediction with Memory](https://mlsanity.com/paper/2404.04808/) (2024)
- [Learning Optical Flow from a Few Matches](https://mlsanity.com/paper/2104.02166/) (2021)

## Built on by (most cited first, 1 of 1)

- [VisTa3D: A Dataset and Benchmark for Thin Object Reconstruction from Vision, Tactile, and 3D Point Clouds](https://mlsanity.com/paper/2608.20740/) (2026)

## Abstract (arXiv)

We propose triangular consistency as a first-principled constraint for optical flow, which is agnostic to network architecture, supervision type, and dataset, and applies to both image-pair and multi-frame settings. This simple but powerful constraint is to compose two flows to induce a third flow and enforce consistency among the three. The composed flows may arise from (i) image pairs, yielding cycle consistency; (ii) multiple video frames, producing longer-range motion through temporal chaining; or (iii) image pairs combined with controlled synthetic transformations, which becomes data augmentation. This triangular consistency introduces negligible computational overhead and requires no additional annotations. Since it is derived directly from the geometry of optical flow, it does not rely on model-specific assumptions and serves as a ``universal'' plug-and-play component for optical flow training. Experiments show consistent improvement across supervised, unsupervised, and transfer learning settings.