PUGS: Physics-Guided Uncertainty Modeling for Underwater Dynamic 3D Gaussian Splatting

Tingjun Li; Yuxi Wang; Guoqiang Zhong; Zhaoxiang Zhang

cs.CVOct 13, 2026

PUGS: Physics-Guided Uncertainty Modeling for Underwater Dynamic 3D Gaussian Splatting

Authors: Tingjun Li, Yuxi Wang, Guoqiang Zhong, Zhaoxiang Zhang

Organizations: College of Computer Science and Technology, Faculty of Information Science and Engineering, Ocean University of China, Qingdao 266100, China · New Laboratory of Pattern Recognition (NLPR), State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences (CASIA), and University of Chinese Academy of Sciences (UCAS), Beijing 100049, China

Abstract

Dynamic 3D Gaussian Splatting (3DGS) provides an efficient framework for dynamic scene reconstruction. Most existing approaches model scene dynamics with deterministic deformation fields, assuming each Gaussian follows a distinct geometric trajectory over time. This assumption breaks down underwater, where light scattering, refraction, marine snow and low visibility create substantial physical ambiguity in captured images. We present PUGS, a physics-guided uncertainty model for underwater dynamic 3DGS. PUGS learns inherent uncertainty induced by underwater image formation and leverages it as a physical signal for dynamic scene modeling. Rather than estimating a single deterministic displacement, it parameterizes each Gaussian's motion as a probability distribution with expected deformation and physical uncertainty. We adopt stochastic deformation optimization to sample Gaussian trajectories via local reparameterization, exploring multiple physically plausible solutions during training. We further propose uncertainty stochastic annealing and a dual-path self-consistency distillation objective, converting stochastic exploration to deterministic reconstruction while preserving temporal coherence. Extensive experiments on underwater dynamic datasets and physics-aware benchmarks demonstrate superior rendering quality, temporal consistency and reconstruction robustness. Our method achieves 1.16 dB PSNR gain over the strongest baseline on UVEB and 3.99 dB on DRUVA.

Figures & tables

Fig. 1: We present PUGS, a method that explicitly models physical uncertainty in dynamic 3D Gaussian splatting. On the challenging underwater sequence, a deterministic deformation-based method (Row 1) entangles structural motion with optical interference, producing floaters, blur, distortion, and ghosting artifacts. In contrast, PUGS (Row 2) learns a per-pixel physical uncertainty signal $\Delta\sigma$ (visualized as heatmaps) that captures where and when the optical medium degrades observation reliability. This uncertainty is annealed over time $\beta(t):1\rightarrow 0$ , enabling the model to progressively resolve physical ambiguity and produce clean, artifact-free renderings that closely match the ground-truth reference.

Fig. 2: Overview of the PUGS Pipeline for Underwater Dynamic Scene Reconstruction. Given a monocular video, SfM initializes a set of canonical Gaussians. To address the observational ambiguities caused by underwater physical disturbances, our deformation field predicts not only the displacement mean $\Delta\boldsymbol{\mu}$ but also the positional uncertainty $\Delta\boldsymbol{\sigma}$ , yielding a complete characterization of the motion distribution. A deterministic rendering path (clean path) and an uncertainty-aware rendering path (uncertainty path) are then constructed in parallel and jointly optimized via a self-consistency distillation constraint. Meanwhile, Gaussians with high uncertainty are adaptively split to enhance local representation capacity, thereby improving the robustness of underwater reconstruction. In this way, underwater dynamics modeling addresses the failure of deterministic deformation fields under ambiguous observations, while uncertainty-guided optimization leverages the learned uncertainty to allocate representation capacity and stabilize training.

	Boat			Streak			Fish			Cave
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	24.03	0.829	0.309	24.53	0.897	0.096	24.75	0.815	0.230	28.53	0.928	0.344
Sea-splat	24.87	0.779	0.337	28.72	0.934	0.058	26.98	0.822	0.262	29.61	0.932	0.269
3D-4DGS	24.22	0.854	0.306	29.04	0.905	0.063	32.03	0.917	0.130	24.73	0.884	0.283
RobustGS	17.81	0.832	0.233	22.95	0.807	0.153	25.58	0.780	0.189	26.14	0.949	0.197
PSF-4D	25.05	0.812	0.320	32.41	0.953	0.044	27.13	0.903	0.242	35.45	0.966	0.139

TABLE I: Quantitative comparison on UVEB dataset. We compare our method to state-of-the-art approaches, including static 3D-GS, Sea-splat, 3D-4DGS, PSF-4D, Light-GS, RobustGS and Deformable-GS. We report PSNR, SSIM, and LPIPS. , , and backgrounds denote the best, second-best, and third-best results, respectively.

Fig. 3: Qualitative Comparison on UVEB dataset. We conduct comparisons across nine scenes and provide zoomed-in views for each scene to examine the rendered reconstruction details, with a particular focus on dynamic content and complex scene regions. Our method consistently produces higher-quality results in both dynamic and static regions.

	A1			A2			A11			A12			Average
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
TiNeuVox	23.05	0.757	0.664	21.74	0.843	0.637	27.02	0.878	0.355	27.59	0.911	0.221	24.85	0.847	0.469
SeaThru-NeRF	26.27	0.778	0.336	20.23	0.694	0.481	27.62	0.916	0.254	26.13	0.883	0.282	25.06	0.818	0.338
4DGaussian	22.84	0.688	0.535	20.93	0.586	0.638	26.84	0.882	0.273	25.84	0.906	0.244	24.11	0.766	0.423
4DGS	20.75	0.736	0.449	19.54	0.678	0.516	24.09	0.938	0.173	25.79	0.956	0.128	22.54	0.827	0.317
WaterSplatting	28.71	0.830	0.376	26.33	0.809	0.406	32.33	0.962	0.207	30.86	0.958	0.201	29.56	0.890	0.298

TABLE II: Quantitative comparison on DRUVA dataset. We compare our method to state-of-the-art approaches, including TiNeuVox, SeaThru-NeRF, 4DGaussian, 4DGS, WaterSplatting and UDF. We report PSNR, SSIM, and LPIPS. , , and backgrounds denote the best, second-best, and third-best results, respectively.

Fig. 4: Qualitative Comparison on DRUVA dataset. We conduct comparisons across two scenes and provide zoomed-in views for each scene to examine the rendered reconstruction details, with a particular focus on dynamic content and complex scene regions. Our method consistently produces higher-quality results in both dynamic and static regions.

	hanok			single flag			pisa			bouncing balls
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$
MoSca	14.80	0.590	0.420	15.30	0.560	0.500	16.70	0.540	0.570	19.90	0.810	0.120
STG	14.80	0.600	0.410	26.00	0.870	0.140	20.10	0.680	0.330	11.90	0.510	0.600
SOM	14.70	0.670	0.400	16.30	0.600	0.240	17.10	0.650	0.410	17.40	0.790	0.140
4DGS	15.50	0.740	0.320	18.00	0.650	0.290	19.30	0.670	0.260	22.70	0.860	0.100
Deformable-GS	16.30	0.780	0.280	18.30	0.680	0.240	20.70	0.720	0.260	19.80	0.770	0.150

TABLE III: Quantitative comparison on dynamic scenes. We compare our method to MoSca, STG, SOM, 4DGS and Deformable-GS. We report PSNR, SSIM, and LPIPS. , , and backgrounds denote the best, second-best, and third-best results, respectively.

Table 8

UQ for 3D Reconstruction

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May 12, 2025J/K move · Enter open · S save

TUGS: Physics-based Compact Representation of Underwater Scenes by Tensorized Gaussian

Shijie Lian, Ziyi Zhang, Hua Li, Laurence Tianruo Yang+3

1Huazhong University of Science and Technology · 2Zhongguancun Academy · 3The Chinese University of Hong Kong, Shenzhen+3

3D Gaussian Splatting Underwater Imaging 3D Reconstruction Underwater 3D Reconstruction Gaussian Splatting

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Underwater 3D scene reconstruction is crucial for multimedia applications in adverse environments, such as underwater robotic perception and navigation. However, the complexity of interactions between light propagation, water medium, and object surfaces poses significant difficulties for existing methods in accurately simulating their interplay. Additionally, expensive training and rendering costs limit their practical application. Therefore, we propose Tensorized Underwater Gaussian Splatting (TUGS), a compact underwater 3D representation based on physical modeling of complex underwater light fields. TUGS includes a physics-based underwater Adaptive Medium Estimation (AME) module, enabling accurate simulation of both light attenuation and backscatter effects in underwater environments, and introduces Tensorized Densification Strategies (TDS) to efficiently refine the tensorized representation during optimization. TUGS is able to render high-quality underwater images with faster rendering speeds and less memory usage. Extensive experiments on real-world underwater datasets have demonstrated that TUGS can efficiently achieve superior reconstruction quality using a limited number of parameters. The code is available at https://liamlian0727.github.io/TUGS

Abstract

UQ for 3D Reconstruction

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