A Theoretical Analysis of a Bilevel Optimization Formulation for Combined Local-Global Optical Flow Models

We present FlowIt, a novel architecture for optical flow estimation that combines global matching with confidence and occlusion-guided refinement. At its core, FlowIt leverages a hierarchical transformer architecture that captures extensive global context, enabling the model to effectively model long-range correspondences. To overcome the limitations of localized matching, we formulate the flow initialization as an optimal transport problem. This formulation yields a highly robust initial flow field, alongside explicitly derived occlusion and confidence maps. These cues are then seamlessly integrated into a guided refinement stage, where the network actively propagates reliable motion estimates from high-confidence regions into ambiguous, low-confidence areas. Extensive experiments across the Sintel, KITTI, Spring, and LayeredFlow datasets validate the effectiveness of our approach. FlowIt achieves state-of-the-art results on the competitive Sintel benchmark and establishes new state-of-the-art cross-dataset zero-shot generalization performance on Sintel, Spring, and LayeredFlow, while also delivering competitive performance on both the KITTI benchmark and KITTI zero-shot generalization settings.

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.

Optical flow methods typically rely on task-specific inductive biases, such as correlation volumes, feature warping, and iterative refinement, among others, to reach high accuracy. While effective, such biases constrain the model to predefined heuristics, which can limit its expressivity and lead to more complex pipelines and additional computational cost. We present FreeFlow, a hierarchical transformer built without any flow-specific components, using instead a single feed-forward encoder--decoder. FreeFlow combines three attention variants: window attention for local processing, shifted-window attention for cross-window information exchange, and a global attention operating at a reduced resolution. The resulting architecture scales naturally with model capacity, enabling a consistent accuracy gain from small to large variants. Despite the absence of standard inductive biases, FreeFlow achieves state-of-the-art results on major benchmarks, including Sintel (0.68/1.48 EPE on Clean/Final), KITTI-2015 (3.23 Fl-all), and Spring (3.192 1px), while remaining memory efficient at 1080p inference.