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Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields
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Proposes Bayes' Rays, a post-hoc Laplace-approximation method that builds a volumetric epistemic uncertainty field for any pretrained NeRF via a spatial deformation-field reparametrization, without retraining.
Problem
Quantifying epistemic uncertainty in pretrained Neural Radiance Fields is either heuristic or computationally expensive, and existing principled methods require changing the NeRF training pipeline.
Approach
Reparametrize a frozen NeRF with a grid-based spatial deformation field and apply a diagonal Laplace approximation using Gauss-Newton-style Fisher information from first derivatives only, yielding a per-location uncertainty field renderable as an extra channel, requiring no retraining or training images.
Key results
- Bayes' Rays uncertainty achieves AUSE comparable to a 10-model ensemble and clearly better than CF-NeRF (e.g., africa 0.27 vs CF-NeRF 0.35, ensemble 0.18), at about 90 seconds of computation.
- For floater removal, Bayes' Rays-best reaches PSNR 18.27 and coverage 0.70 vs Nerfbusters 17.99 and 0.63, while taking 1.6 min vs 20 min.
- Architecture-independent: qualitatively similar uncertainty maps on Mip-NeRF, Instant-NGP and Nerfacto for the Lego scene.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Bayes′Rays uncertainty for floater cleanup instead of Nerfbusters | Nerfacto · NeRF cleanup dataset | PSNR: 17.99 -> 18.27 | Helped |
| Use Bayes′Rays uncertainty for floater cleanup instead of Nerfbusters | Nerfacto · NeRF cleanup dataset | Coverage: 0.63 -> 0.70 | Helped |
| Estimate uncertainty with Bayes′Rays rather than CF-NeRF | Nerfacto · ScanNet and Light Field scenes | AUSE | Helped |
| Use grid resolution M > 256 instead of a smaller grid (ablation) | Bayes′Rays · Lego, NeRF Synthetic | AUSE | No clear effect |
| Increase deformation-grid resolution from a very low value (ablation) | Bayes′Rays · Lego, NeRF Synthetic | surface uncertainty detection | Helped |
| Lower the uncertainty threshold during rendering (ablation) | Bayes′Rays cleanup · garbage scene, Nerfbusters dataset | floater removal | Helped |
| Apply Bayes′Rays to Mip-NeRF, Instant-NGP, or Nerfacto architectures (ablation) | Bayes′Rays · Lego, NeRF Synthetic | uncertainty visualization | No clear effect |
Surprising findings
- Uncertainty estimated from a single pass without retraining closely matches a costly 10-model ensemble on depth-error sparsification.
- Very low grid resolutions (M=32) underestimate uncertainty, with diminishing returns beyond M=256.
Limitations
- Only captures epistemic uncertainty; aleatoric effects such as inconsistencies between views are not captured.
- Uniform grid discretization of the deformation field incurs high memory cost in low-interest regions.
- Only diagonal of the Hessian is used, ignoring inter-parameter correlations.
Experimental setup
Datasets: ScanNet Light Field dataset NeRF Synthetic (Lego) Nerfbusters dataset
Benchmarks: ScanNet Light Field dataset Nerfbusters dataset
Metrics: AUSE PSNR SSIM LPIPS Coverage Processing time
Baselines: CF-NeRF Deep Ensembles (10 Nerfacto) Nerfbusters
Builds on: Laplace approximation (Ritter et al.) Nerfacto NeRF photogrammetry covariance estimation
Closest papers by meaning
- Neural Visibility Field for Uncertainty-Driven Active Mapping (CVPR 2024 · similarity 0.89)
- ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Field (NeurIPS 2024 · similarity 0.86)
- Alpha Invariance: On Inverse Scaling Between Distance and Volume Density in Neural Radiance Fields (CVPR 2024 · similarity 0.85)
- Rad-NeRF: Ray-decoupled Training of Neural Radiance Field (NeurIPS 2024 · similarity 0.85)
- Learning Robust Generalizable Radiance Field with Visibility and Feature Augmented Point Representation (ICLR 2024 · similarity 0.85)
- NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction (CVPR 2025 · similarity 0.85)
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