# Learning Optical Flow Field via Neural Ordinary Differential Equation

arXiv: https://arxiv.org/abs/2506.03290 · HTML: https://mlsanity.com/paper/2506.03290/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [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)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Perceiver IO: A General Architecture for Structured Inputs & Outputs](https://mlsanity.com/paper/2107.14795/) (2021)
- [Optical Flow Estimation using a Spatial Pyramid Network](https://mlsanity.com/paper/1611.00850/) (2016)
- [GMFlow: Learning Optical Flow via Global Matching](https://mlsanity.com/paper/2111.13680/) (2021)
- [FlowFormer: A Transformer Architecture for Optical Flow](https://mlsanity.com/paper/2203.16194/) (2022)
- [Unifying Flow, Stereo and Depth Estimation](https://mlsanity.com/paper/2211.05783/) (2022)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Learning to Estimate Hidden Motions with Global Motion Aggregation](https://mlsanity.com/paper/2104.02409/) (2021)
- [The Surprising Effectiveness of Diffusion Models for Optical Flow and Monocular Depth Estimation](https://mlsanity.com/paper/2306.01923/) (2023)
- [Models Matter, So Does Training: An Empirical Study of CNNs for Optical Flow Estimation](https://mlsanity.com/paper/1809.05571/) (2018)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [A Lightweight Optical Flow CNN - Revisiting Data Fidelity and Regularization](https://mlsanity.com/paper/1903.07414/) (2019)
- [Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE](https://mlsanity.com/paper/2006.02493/) (2020)
- [Global Matching with Overlapping Attention for Optical Flow Estimation](https://mlsanity.com/paper/2203.11335/) (2022)
- [Deep Equilibrium Optical Flow Estimation](https://mlsanity.com/paper/2204.08442/) (2022)
- [Imposing Consistency for Optical Flow Estimation](https://mlsanity.com/paper/2204.07262/) (2022)

## Abstract (arXiv)

Recent works on optical flow estimation use neural networks to predict the flow field that maps positions of one image to positions of the other. These networks consist of a feature extractor, a correlation volume, and finally several refinement steps. These refinement steps mimic the iterative refinements performed by classical optimization algorithms and are usually implemented by neural layers (e.g., GRU) which are recurrently executed for a fixed and pre-determined number of steps. However, relying on a fixed number of steps may result in suboptimal performance because it is not tailored to the input data. In this paper, we introduce a novel approach for predicting the derivative of the flow using a continuous model, namely neural ordinary differential equations (ODE). One key advantage of this approach is its capacity to model an equilibrium process, dynamically adjusting the number of compute steps based on the data at hand. By following a particular neural architecture, ODE solver, and associated hyperparameters, our proposed model can replicate the exact same updates as recurrent cells used in existing works, offering greater generality. Through extensive experimental analysis on optical flow benchmarks, we demonstrate that our approach achieves an impressive improvement over baseline and existing models, all while requiring only a single refinement step.