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

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.