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Variational Multi-scale Representation for Estimating Uncertainty in 3D Gaussian Splatting
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Proposes variational multi-scale 3D Gaussians with a learned offset table (sharing base attributes) to estimate posterior and predictive uncertainty for 3DGS, enabling floater removal.
Problem
3D Gaussian Splatting lacks the ability to quantify uncertainty over its reconstruction and predictions, which matters for robotics mapping, navigation and view-synthesis confidence.
Approach
Spawn finer multi-scale Gaussians from base Gaussians via a learned offset table that offsets only position, scale and opacity while sharing color and rotation; the offset posterior is learned by variational inference with a multi-scale prior, giving diverse parameter-space samples efficiently.
Key results
- On the LF dataset, depth uncertainty AUSE averages 0.19, the best among compared methods, versus 0.20 for Ensemble GS (x10) and 0.23 for Bayes' Ray.
- On LLFF, the method achieves the best rendered-image NLL (0.23) versus 0.26 for Ensemble GS (x10), while its PSNR (23.97) trails Ensemble GS (24.54).
- Removing Gaussians with large posterior uncertainty removes background floaters on Mip-NeRF 360 scenes while keeping the foreground object intact after deleting 70% of Gaussians.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use variational multi-scale 3D Gaussians for uncertainty estimation | 3DGS · LF depth uncertainty (Average) | AUSE: 0.20 -> 0.19 | Helped |
| Use variational multi-scale 3D Gaussians | 3DGS · LF | SSIM: 0.902 -> 0.914 | Helped |
| Use variational multi-scale 3D Gaussians instead of Ensemble GS | 3DGS · LF | PSNR: 27.64 -> 27.39 | Hurt |
| Use variational multi-scale 3D Gaussians instead of Ensemble GS | 3DGS · LF | LPIPS: 0.088 -> 0.101 | Hurt |
| Use variational multi-scale 3D Gaussians instead of Ensemble GS | 3DGS · LF | AUSE: 0.29 -> 0.26 | Helped |
| Use uncertainty to select images instead of random selection | 3DGS active data acquisition · LLFF | PSNR: 20.97 -> 21.35 | Helped |
| Use uncertainty to select images instead of random selection | 3DGS active data acquisition · LLFF | LPIPS: 0.234 -> 0.212 | Helped |
| Increase the spawned finer-Gaussian count from 1 to 10 (ablation) | Variational multi-scale 3DGS · LLFF (8-scene average) | AUSE: 0.37 -> 0.32 | Helped |
| Increase the spawned finer-Gaussian count from 1 to 10 (ablation) | Variational multi-scale 3DGS · LLFF (8-scene average) | SSIM: 0.792 -> 0.806 | Helped |
Surprising findings
- Ensemble GS with 10 models reaches comparable or better rendering PSNR than the proposed method on LF and LLFF, so the method's advantage is mainly in uncertainty calibration and efficiency.
Limitations
- Active learning application is only a preliminary experiment, which the authors acknowledge as a limitation.
- Rendering PSNR is lower than the ensemble baseline on LLFF.
Experimental setup
Datasets: LF dataset LLFF dataset Mip-NeRF 360 dataset
Benchmarks: LF dataset LLFF dataset Mip-NeRF 360
Metrics: AUSE NLL PSNR SSIM LPIPS
Baselines: CF-NeRF S-NeRF Bayes' Ray Ensemble GS (x10) FisherRF
Builds on: 3D Gaussian Splatting Stochastic NeRF CF-NeRF Bayes' Ray
Closest papers by meaning
- Metropolis-Hastings Sampling for 3D Gaussian Reconstruction (NeurIPS 2025 · similarity 0.90)
- Evolving High-Quality Rendering and Reconstruction in a Unified Framework with Contribution-Adaptive Regularization (CVPR 2025 · similarity 0.89)
- GaussianSpa: An "Optimizing-Sparsifying" Simplification Framework for Compact and High-Quality 3D Gaussian Splatting (CVPR 2025 · similarity 0.89)
- PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting (CVPR 2025 · similarity 0.89)
- 3D Gaussian Splatting as Markov Chain Monte Carlo (NeurIPS 2024 · similarity 0.89)
- VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment (NeurIPS 2025 · similarity 0.88)
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