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

Thai Duy Nguyen; Haitian Zhang; Addison Lin Wang

cs.CVSep 29, 2026

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

Authors: Thai Duy Nguyen, Haitian Zhang, Addison Lin Wang

Organizations: Nanyang Technological University, Singapore.

Abstract

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.

Figures & tables

Fig. 1: Highlight of our motion disentangling framework. In dynamic scenarios, between frames there are two types of motion being entangled together: the camera motion (from $view_{1}$ to $view_{2}$ ), and the scene motion (from state at $t_{1}$ to $t_{2}$ ). For efficient motion supervision, such two motions need to be disentangle. Our method uses Deformable 3DGS to render an intermediate image at $(view_{1},t_{2})$ , such that its motion relative to each input frame isolates a single motion component by keeping either the viewpoint or the scene state fixed during motion estimation.

Fig. 3: Overview of the proposed DispFlow-GS framework. The optimization consists of two components: photometric loss and motion loss. The photometric loss is the standard rendered image loss. The motion loss is defined by our Displacement Flow Supervision, where displacement flow is obtained by splatting per-Gaussian 3D displacements onto the image plane and supervising them against scene motion.

Fig. 4: Illustration of scene motion calculation. For an input pair $(view_{1},t_{1})$ and $(view_{2},t_{2})$ , total motion includes scene and camera motion. MotionGS estimates cross-view flow and subtracts camera motion, which is error-prone due to large cross-view displacements. Instead, we render an intermediate frame at $(view_{1},t_{2})$ and compute flow between $(view_{1},t_{1})$ and $(view_{1},t_{2})$ to isolate scene motion under a fixed viewpoint.

	Sieve			Plate			Bell			Press
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
3D - GS [ 1 ]	23.16	0.8203	0.2247	16.14	0.6970	0.4093	21.01	0.7885	0.2503	22.89	0.8163	0.2904
TiNeuVox [ 38 ]	21.49	0.8265	0.3176	20.58	0.8027	0.3317	23.08	0.8242	0.2568	24.47	0.8613	0.3001
HyperNeRF [ 16 ]	25.43	0.8798	0.1645	18.93	0.7709	0.2940	23.06	0.8097	0.2052	26.15	0.8897	0.1959
NeRF - DS [ 15 ]	25.78	0.8900	0.1472	20.54	0.8042	0.1996	23.19	0.8212	0.1867	25.72	0.8618	0.2047
Deformable - 3DGS [ 7 ]	25.27	0.8682	0.1532	20.51	0.8090	0.2271	25.07	0.8446	0.1725	25.45	0.8619	0.1941

TABLE I: Quantitative comparison using image-based metrics on the NeRF-DS dataset per scene. We highlight the best and second-best results in each scene.

	Sieve		Plate		Bell		Press
Method	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$
Deformable - 3DGS [ 7 ]	0.4220	0.6320	0.7514	0.7088	0.8562	0.7608	0.7346	0.6994
MotionGS [ 12 ]	0.5905	0.6600	0.7149	0.7095	0.8236	0.7395	0.7398	0.6867
DispFlow-GS	0.8724	0.6957	0.9204	0.7573	0.8936	0.7769	0.9128	0.7133
	Cup		As		Basin		Mean
Method	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$

TABLE II: Quantitative comparison using motion-based metrics on the NeRF-DS dataset per scene.

	Chicken				Banana				Mean
Method	PSNR $\uparrow$	SSIM $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	MMAP $\uparrow$	DRC $\uparrow$
HyperNeRF [ 16 ]	27.40	0.630	–	–	22.10	0.720	–	–	24.80	0.680	–	–
TiNeuVox [ 38 ]	28.20	0.790	–	–	24.40	0.640	–	–	26.30	0.720	–	–
Deformable - 3DGS [ 7 ]	23.58	0.646	0.529	0.729	25.16	0.831	0.749	0.760	24.37	0.738	0.639	0.744
MotionGS [ 12 ]	23.44	0.638	0.625	0.729	24.90	0.829	0.751	0.752	24.17	0.733	0.688	0.741
DispFlow-GS	23.66	0.649	0.664	0.743	24.97	0.830	0.774	0.758	24.31	0.739	0.719	0.750

TABLE III: Quantitative comparison on the HyperNeRF dataset per scene.

Fig. 5: Qualitative results on representative scenes of NeRF-DS dataset. For each scene, the top row shows the rendered images, while the bottom row shows the corresponding Displacement Flow.

Fig. 6: Qualitative results on ‘chicken’ scene of the HyperNeRF dataset.

Method	DF	MD	TS	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	MMAP $\uparrow$	DRC $\uparrow$
Baseline				23.76	0.8485	0.1846	0.6497	0.6660
1	✓			23.63	0.8406	0.1941	0.6306	0.6455
2	✓		✓	23.77	0.8462	0.1878	0.6817	0.6577
3	✓	✓		23.62	0.8467	0.1902	0.9316	0.7261
Ours	✓	✓	✓	23.80	0.8485	0.1869	0.9015	0.7081

TABLE IV: Ablation on key components: displacement flow (DF), motion decomposition (MD), and training scheduling (TS).

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	MMAP $\uparrow$	DRC $\uparrow$
Gaussian Flow + Indirect Scene Motion (MotionGS)	23.75	0.8290	0.2364	0.6825	0.6685
Gaussian Flow + Direct Scene Motion	23.85	0.8485	0.1846	0.6317	0.6673
Displacement Flow + Indirect Scene Motion	23.92	0.8498	0.1833	0.7258	0.6728
Displacement Flow + Direct Scene Motion (Ours)	23.80	0.8485	0.1869	0.9015	0.7081

TABLE V: Ablation on motion representations and supervision targets.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	MMAP $\uparrow$	DRC $\uparrow$
Different flow model (RAFT [ 39 ] )	23.78	0.8488	0.1847	0.9024	0.7083
Different flow model (MDFlow [ 40 ] )	23.73	0.8476	0.1865	0.8084	0.6824
Smaller motion loss weight ( $\alpha$ = 0.02)	23.78	0.8478	0.1873	0.8206	0.6866
Larger motion loss weight ( $\alpha$ = 0.5)	23.61	0.8464	0.1910	0.9269	0.7216
Motion decomposition in reverse order	23.87	0.8472	0.1892	0.5566	0.6473
Motion mask filtering	23.78	0.8475	0.1889	0.8629	0.7063

TABLE VI: Ablation on flow backbones, loss weights, and motion masks.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	MMAP $\uparrow$	DRC $\uparrow$
Max-Absolute Normalization	23.75	0.8485	0.1869	0.8970	0.7041
Z-score Normalization	23.39	0.8388	0.2024	0.8926	0.6973
Interquartile Range Normalization	23.76	0.8483	0.1862	0.9254	0.7115
Min-Max Normalization (Ours)	23.80	0.8485	0.1869	0.9015	0.7081

TABLE VII: Ablation study on motion normalization strategies.

Fig. 7: Failure cases on the HyperNeRF dataset.

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