# Eulerian Motion Guidance: Robust Image Animation via Bidirectional Geometric Consistency

arXiv: https://arxiv.org/abs/2605.06280 · HTML: https://mlsanity.com/paper/2605.06280/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Video generation, one of 14 directions in Diffusion models.
- Builds on 28 of its 44 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

- Diffusion models / [Video generation](https://mlsanity.com/diffusion/video-generation/)

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [Animate Anyone: Consistent and Controllable Image-to-Video Synthesis for Character Animation](https://mlsanity.com/paper/2311.17117/) (2023)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [Generating Videos with Scene Dynamics](https://mlsanity.com/paper/1609.02612/) (2016)
- [DragNUWA: Fine-grained Control in Video Generation by Integrating Text, Image, and Trajectory](https://mlsanity.com/paper/2308.08089/) (2023)
- [LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation](https://mlsanity.com/paper/2303.17189/) (2023)
- [Learning Blind Video Temporal Consistency](https://mlsanity.com/paper/1808.00449/) (2018)
- [Video models are zero-shot learners and reasoners](https://mlsanity.com/paper/2509.20328/) (2025)
- [Hallo: Hierarchical Audio-Driven Visual Synthesis for Portrait Image Animation](https://mlsanity.com/paper/2406.08801/) (2024)
- [EchoMimic: Lifelike Audio-Driven Portrait Animations through Editable Landmark Conditions](https://mlsanity.com/paper/2407.08136/) (2024)
- [Conditional Image-to-Video Generation with Latent Flow Diffusion Models](https://mlsanity.com/paper/2303.13744/) (2023)
- [StyleHEAT: One-Shot High-Resolution Editable Talking Face Generation via Pre-trained StyleGAN](https://mlsanity.com/paper/2203.04036/) (2022)
- [Hallo3: Highly Dynamic and Realistic Portrait Image Animation with Video Diffusion Transformer](https://mlsanity.com/paper/2412.00733/) (2024)
- [Go-with-the-Flow: Motion-Controllable Video Diffusion Models Using Real-Time Warped Noise](https://mlsanity.com/paper/2501.08331/) (2025)
- [MOFA-Video: Controllable Image Animation via Generative Motion Field Adaptions in Frozen Image-to-Video Diffusion Model](https://mlsanity.com/paper/2405.20222/) (2024)
- [FlowVid: Taming Imperfect Optical Flows for Consistent Video-to-Video Synthesis](https://mlsanity.com/paper/2312.17681/) (2023)
- [SG-I2V: Self-Guided Trajectory Control in Image-to-Video Generation](https://mlsanity.com/paper/2411.04989/) (2024)
- [Image Conductor: Precision Control for Interactive Video Synthesis](https://mlsanity.com/paper/2406.15339/) (2024)
- [ATI: Any Trajectory Instruction for Controllable Video Generation](https://mlsanity.com/paper/2505.22944/) (2025)
- [Cinemo: Consistent and Controllable Image Animation with Motion Diffusion Models](https://mlsanity.com/paper/2407.15642/) (2024)
- [FaceShot: Bring Any Character into Life](https://mlsanity.com/paper/2503.00740/) (2025)
- [OCAI: Improving Optical Flow Estimation by Occlusion and Consistency Aware Interpolation](https://mlsanity.com/paper/2403.18092/) (2024)
- [PoseTraj: Pose-Aware Trajectory Control in Video Diffusion](https://mlsanity.com/paper/2503.16068/) (2025)
- [Stable Video-Driven Portraits](https://mlsanity.com/paper/2509.17476/) (2025)
- [FactorPortrait: Controllable Portrait Animation via Disentangled Expression, Pose, and Viewpoint](https://mlsanity.com/paper/2512.11645/) (2025)

## Abstract (arXiv)

Recent advancements in image animation have utilized diffusion models to breathe life into static images. However, existing controllable frameworks typically rely on Lagrangian motion guidance, where optical flow is estimated relative to the initial frame. This paper revisits the same optical-flow primitive through a more local supervision design: we use adjacent-frame Eulerian motion fields to guide generation, where the motion signal always describes a short temporal hop. This shift enables parallelized training and provides bounded-error supervision throughout the generation process. To mitigate the drift artifacts common in adjacent frame generation, we introduce a Bidirectional Geometric Consistency mechanism, which computes a forward-backward cycle check to mathematically identify and mask occluded regions, preventing the model from learning incorrect warping objectives. Extensive experiments demonstrate that our approach accelerates training, preserves temporal coherence, and reduces dynamic artifacts compared to reference-based baselines. The code, model, and data have been made available at https://nguyentthong.github.io/eulerian/