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

arXiv: https://arxiv.org/abs/2610.17936 · HTML: https://mlsanity.com/paper/2610.17936/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 73 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 30 of 49)

- [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)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [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)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [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)
- [Shape of Motion: 4D Reconstruction from a Single Video](https://mlsanity.com/paper/2407.13764/) (2024)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [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)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [Dynamic Gaussian Marbles for Novel View Synthesis of Casual Monocular Videos](https://mlsanity.com/paper/2406.18717/) (2024)
- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [NeuralDiff: Segmenting 3D objects that move in egocentric videos](https://mlsanity.com/paper/2110.09936/) (2021)
- [WaterSplatting: Fast Underwater 3D Scene Reconstruction Using Gaussian Splatting](https://mlsanity.com/paper/2408.08206/) (2024)
- [Gaussian Splashing: Unified Particles for Versatile Motion Synthesis and Rendering](https://mlsanity.com/paper/2401.15318/) (2024)
- [SeaSplat: Representing Underwater Scenes with 3D Gaussian Splatting and a Physically Grounded Image Formation Model](https://mlsanity.com/paper/2409.17345/) (2024)
- [Diving Deeper into Underwater Image Enhancement: A Survey](https://mlsanity.com/paper/1907.07863/) (2019)
- [SAGD: Boundary-Enhanced Segment Anything in 3D Gaussian via Gaussian Decomposition](https://mlsanity.com/paper/2401.17857/) (2024)
- [WaterNeRF: Neural Radiance Fields for Underwater Scenes](https://mlsanity.com/paper/2209.13091/) (2022)
- [Momentum-GS: Momentum Gaussian Self-Distillation for High-Quality Large Scene Reconstruction](https://mlsanity.com/paper/2412.04887/) (2024)
- [UW-GS: Distractor-Aware 3D Gaussian Splatting for Enhanced Underwater Scene Reconstruction](https://mlsanity.com/paper/2410.01517/) (2024)

## Abstract (arXiv)

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.