# DispFlow-GS: Displacement Flow Supervision with Motion Disentangling for Monocular Deformable 3D Gaussian Splatting

arXiv: https://arxiv.org/abs/2609.36940 · HTML: https://mlsanity.com/paper/2609.36940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 40 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 36)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Fast Dynamic Radiance Fields with Time-Aware Neural Voxels](https://mlsanity.com/paper/2205.15285/) (2022)
- [Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2312.16812/) (2023)
- [GMFlow: Learning Optical Flow via Global Matching](https://mlsanity.com/paper/2111.13680/) (2021)
- [DynIBaR: Neural Dynamic Image-Based Rendering](https://mlsanity.com/paper/2211.11082/) (2022)
- [Tensor4D : Efficient Neural 4D Decomposition for High-fidelity Dynamic Reconstruction and Rendering](https://mlsanity.com/paper/2211.11610/) (2022)
- [Gaussian-Flow: 4D Reconstruction with Dynamic 3D Gaussian Particle](https://mlsanity.com/paper/2312.03431/) (2023)
- [MoSca: Dynamic Gaussian Fusion from Casual Videos via 4D Motion Scaffolds](https://mlsanity.com/paper/2405.17421/) (2024)
- [3DGStream: On-the-Fly Training of 3D Gaussians for Efficient Streaming of Photo-Realistic Free-Viewpoint Videos](https://mlsanity.com/paper/2403.01444/) (2024)
- [NeRF-DS: Neural Radiance Fields for Dynamic Specular Objects](https://mlsanity.com/paper/2303.14435/) (2023)
- [Motion-aware 3D Gaussian Splatting for Efficient Dynamic Scene Reconstruction](https://mlsanity.com/paper/2403.11447/) (2024)
- [GaussianFlow: Splatting Gaussian Dynamics for 4D Content Creation](https://mlsanity.com/paper/2403.12365/) (2024)
- [MotionGS: Exploring Explicit Motion Guidance for Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2410.07707/) (2024)
- [A Compact Dynamic 3D Gaussian Representation for Real-Time Dynamic View Synthesis](https://mlsanity.com/paper/2311.12897/) (2023)
- [Flow4D: Leveraging 4D Voxel Network for LiDAR Scene Flow Estimation](https://mlsanity.com/paper/2407.07995/) (2024)
- [SplatFlow: Self-Supervised Dynamic Gaussian Splatting in Neural Motion Flow Field for Autonomous Driving](https://mlsanity.com/paper/2411.15482/) (2024)
- [RoMo: Robust Motion Segmentation Improves Structure from Motion](https://mlsanity.com/paper/2411.18650/) (2024)
- [DualAD: Disentangling the Dynamic and Static World for End-to-End Driving](https://mlsanity.com/paper/2406.06264/) (2024)

## Abstract (arXiv)

Accurate dynamic scene reconstruction is important for robotic perception, where temporally consistent representations of dynamic environments are essential. Deformable 3D Gaussian Splatting (3DGS) models dynamic scenes through deformation fields, and recent methods incorporate motion supervision by aligning rendered Gaussian flow with optical flow. However, we find that such Gaussian-flow-based supervision provides only limited improvements in motion modeling. We identify a fundamental limitation of this supervision paradigm, namely a domain gap between rendered Gaussian flow and optical flow. To address this limitation, we propose a motion supervision framework built on Displacement Flow, which splats per-Gaussian 3D displacements onto the image plane to provide direct and stable optimization signals. We further disentangle scene motion from camera motion via intermediate-view rendering, enabling more reliable motion priors and targeted constraints on deformation and geometry. We also observe a discrepancy between motion fidelity and image-based evaluation, where improved motion awareness does not necessarily translate into better rendered image quality or higher image-based metric scores. Motivated by this mismatch, we introduce Deformation-Rendering Consistency (DRC), a motion-aware metric that measures the alignment between predicted deformation and rendering improvement. Experiments on dynamic scene benchmarks show substantial improvements in motion localization and motion--rendering consistency, reaching up to 39% and 6%, respectively, while image-based metrics change by only about 0.1%. These results confirm the observed mismatch between motion fidelity and image-based evaluation, demonstrating the significance of DRC for motion-aware evaluation.