Evidential Neural Radiance Fields

Ruxiao Duan; Alex Wong

cs.CVFeb 27, 2026

Evidential Neural Radiance Fields

Authors: Ruxiao Duan, Alex Wong

Organizations: Yale University

Abstract

Understanding sources of uncertainty is fundamental to trustworthy three-dimensional scene modeling. While recent advances in neural radiance fields (NeRFs) achieve impressive accuracy in scene reconstruction and novel view synthesis, the lack of uncertainty estimation significantly limits their deployment in safety-critical settings. Existing uncertainty quantification methods for NeRFs fail to separately capture both aleatoric and epistemic uncertainties. Among those that do quantify one or the other, many of them either compromise rendering quality or incur significant computational overhead to obtain uncertainty estimates. To address these issues, we introduce Evidential Neural Radiance Fields, a probabilistic approach that seamlessly integrates with the NeRF rendering process, enabling direct quantification of both aleatoric and epistemic uncertainties from a single forward pass. We compare multiple uncertainty quantification methods on three standardized benchmarks, where our approach demonstrates state-of-the-art scene reconstruction fidelity and uncertainty estimation quality. Code is available at https://github.com/KerryDRX/EvidentialNeRF.

Figures & tables

Figure 1: Scene reconstruction along with its aleatoric and epistemic uncertainties rendered by Evidential NeRF from a scene in the wild. AU arises from intrinsic data variability in the training images, including radiance variation (e.g., sky regions due to changing illumination), high-frequency regions (e.g., object edges), and the presence of transient objects (e.g., pedestrians). EU indicates the model’s lack of knowledge, prominently appearing in occluded regions where training supervision is insufficient (e.g., the trees occluded by the gate).

Figure 2: Evolution of NeRF pipeline across three levels of probabilistic formulations. $N$ points sampled along the camera ray give $N$ pairs of spatial location and viewing direction, which are passed to the NeRF model for prediction. Level 1: Vanilla NeRF predicts only point density and color, resulting in a deterministic pixel color without any uncertainty estimate. Level 2: Normal NeRF assumes the point and pixel colors follow normal distributions, quantifying aleatoric uncertainty of rendered color. Level 3: Evidential NeRF assumes the pixel color has random mean and variance following an evidential distribution, quantifying both aleatoric and epistemic uncertainties.

Dataset	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	NLL $\downarrow$	AUSE RMSE $\downarrow$	AUSE MAE $\downarrow$
LF [ 48 ]	Baseline	28.5538	0.9172	0.0465
	Dropout [ 7 ]	28.1137	0.9061	0.0569	3.6670	0.0125	0.0049
	Normal [ 18 ]	28.0064	0.9165	0.0531	0.4425	0.0090	0.0029
	MoL [ 36 ]	28.2200	0.9095	0.0672	-2.5393	0.0084	0.0029
	Ensembles [ 22 ]	29.3779	0.9308	0.0411	0.3245	0.0070	0.0026
	DANE [ 41 ]	29.3779	0.9308	0.0411	-0.4317	0.0101	0.0039

Table 1: Quantitative results of scene reconstruction and uncertainty quantification on three datasets, averaged over three independent runs. Colored cells denote the first , second , and third best results. See per-scene statistics with standard deviations in supplementary Section 10 .

Figure 3: Qualitative comparison on two example scenes, with image reconstructions, error maps, and uncertainty maps. Histogram equalization is conducted on the error maps to highlight the error regions. Our method’s uncertainty is total uncertainty. In general, our method achieves better reconstruction accuracy and produces uncertainty maps that are more consistent with prediction errors.

Figure 4: Test uncertainties vs. training sample size on Android .

Mode	Baseline	Dropout	Normal	MoL	Ens.	DANE	Ours
Train/min. $\downarrow$	11.84	88.54	12.22	12.71	59.22	59.22	13.57
Infer/FPS $\uparrow$	4.88	0.09	4.71	4.42	0.96	0.96	4.67

Table 2: Average training time per

30k

steps and inference FPS of baseline nerfacto and different UQ methods on an A6000 GPU.

Figure 5: A case where AU dominates EU. The highly reflective surface of the display case in the foreground incurs specular reflections. AU arises due to the presence of data noise caused by the inconsistency of light across different training views.

Figure 6: A case where EU dominates AU. The model is trained only by $5$ images from the front and asked to render the scene from all the viewing angles. EU arises due to the lack of knowledge during training on the views out of the training distribution.

Figure 7: Scene cleaning based on aleatoric uncertainty as a post-processing step for floater removal. Points with AU above a certain threshold have their density reduced to become more transparent. By reducing the threshold, more artifacts can be eliminated.

Scene

Africa

Basket

Statue

Torch

Fern

Flower

Fortress

Horns

Leaves

Orchids

Room

T-Rex

Android

Crab

Statue

Yoda

\lambda_{\text{reg}}

5e-3

1e-1

1e-3

1e0

5e-2

1e0

5e-1

5e0

1e0

5e-1

5e0

5e-3

5e-4

1e-4

1e-5

Table 3: The regularization coefficients used in each scene of LF, LLFF, and RobustNeRF datasets.

Figure 10: Aleatoric and epistemic uncertainties of scenes with transient objects. The red bounding boxes delineate the erroneous artifacts in test renderings caused by transients in the training views. If the model fails to suppress the floaters, both AU and EU are elevated on the transients; If the model resolves the transience, only AU is higher on the regions where the training transients were once present.

Scene	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	NLL $\downarrow$	AUSE RMSE $\downarrow$	AUSE MAE $\downarrow$
	Baseline	26.5406 $\pm$ 0.1903	0.9019 $\pm$ 0.0009	0.0565 $\pm$ 0.0010
	Dropout	26.6798 $\pm$ 0.0205	0.8986 $\pm$ 0.0007	0.0590 $\pm$ 0.0014	4.0201 $\pm$ 0.2676	0.0148 $\pm$ 0.0003	0.0064 $\pm$ 0.0001
	Normal	27.4766 $\pm$ 1.5843	0.9028 $\pm$ 0.0192	0.0608 $\pm$ 0.0210	-1.4911 $\pm$ 0.6587	0.0078 $\pm$ 0.0023	0.0033 $\pm$ 0.0004
Africa	MoL	28.0663 $\pm$ 0.6656	0.9023 $\pm$ 0.0082	0.0614 $\pm$ 0.0056	-2.3375 $\pm$ 0.0088	0.0069 $\pm$ 0.0001	0.0035 $\pm$ 0.0001
	Ensembles	27.0083 $\pm$ 0.0652	0.9171 $\pm$ 0.0003	0.0491 $\pm$ 0.0006	0.0871 $\pm$ 0.1899	0.0087 $\pm$ 0.0005	0.0037 $\pm$ 0.0001
	DANE	27.0083 $\pm$ 0.0652	0.9171 $\pm$ 0.0003	0.0491 $\pm$ 0.0006	-0.9581 $\pm$ 0.1721	0.0139 $\pm$ 0.0010	0.0059 $\pm$ 0.0003

Table 4: Mean and standard deviation of quantitative metrics over three runs on LF.

Scene	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	NLL $\downarrow$	AUSE RMSE $\downarrow$	AUSE MAE $\downarrow$
	Baseline	20.1069 $\pm$ 0.1190	0.5685 $\pm$ 0.0005	0.3617 $\pm$ 0.0050
	Dropout	19.1317 $\pm$ 0.1808	0.5153 $\pm$ 0.0059	0.4432 $\pm$ 0.0060	46.5072 $\pm$ 8.3738	0.0517 $\pm$ 0.0016	0.0294 $\pm$ 0.0020
	Normal	20.1763 $\pm$ 0.3308	0.5905 $\pm$ 0.0115	0.3273 $\pm$ 0.0133	47.5151 $\pm$ 1.6352	0.0349 $\pm$ 0.0014	0.0193 $\pm$ 0.0005
Fern	MoL	18.2953 $\pm$ 0.6532	0.5222 $\pm$ 0.0298	0.4279 $\pm$ 0.0406	1.3336 $\pm$ 0.2902	0.0605 $\pm$ 0.0157	0.0257 $\pm$ 0.0078
	Ensembles	20.7328 $\pm$ 0.0591	0.6134 $\pm$ 0.0016	0.3462 $\pm$ 0.0019	3.2024 $\pm$ 0.4579	0.0297 $\pm$ 0.0004	0.0148 $\pm$ 0.0002
	DANE	20.7328 $\pm$ 0.0591	0.6134 $\pm$ 0.0016	0.3462 $\pm$ 0.0019	2.6334 $\pm$ 0.4099	0.0332 $\pm$ 0.0002	0.0172 $\pm$ 0.0001

Table 5: Mean and standard deviation of quantitative metrics over three runs on LLFF.

Scene	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	NLL $\downarrow$	AUSE RMSE $\downarrow$	AUSE MAE $\downarrow$
	Baseline	13.6976 $\pm$ 0.1464	0.2557 $\pm$ 0.0155	0.4167 $\pm$ 0.0066
	Dropout	13.9549 $\pm$ 0.2228	0.2423 $\pm$ 0.0248	0.4235 $\pm$ 0.0211	141.2669 $\pm$ 12.2890	0.1072 $\pm$ 0.0025	0.0618 $\pm$ 0.0024
	Normal	13.3743 $\pm$ 0.0707	0.2525 $\pm$ 0.0111	0.4239 $\pm$ 0.0075	104.3151 $\pm$ 41.1687	0.1064 $\pm$ 0.0013	0.0553 $\pm$ 0.0009
Leaves	MoL	12.8939 $\pm$ 0.1964	0.2408 $\pm$ 0.0179	0.4276 $\pm$ 0.0162	4.1014 $\pm$ 0.2543	0.1266 $\pm$ 0.0053	0.0674 $\pm$ 0.0044
	Ensembles	14.2397 $\pm$ 0.0569	0.2960 $\pm$ 0.0069	0.4319 $\pm$ 0.0047	12.3460 $\pm$ 0.5912	0.0915 $\pm$ 0.0010	0.0471 $\pm$ 0.0007
	DANE	14.2397 $\pm$ 0.0569	0.2960 $\pm$ 0.0069	0.4319 $\pm$ 0.0047	11.6017 $\pm$ 0.1579	0.0928 $\pm$ 0.0009	0.0482 $\pm$ 0.0006

Table 6: Mean and standard deviation of quantitative metrics over three runs on LLFF.

Scene	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	NLL $\downarrow$	AUSE RMSE $\downarrow$	AUSE MAE $\downarrow$
	Baseline	22.8865 $\pm$ 0.0476	0.7691 $\pm$ 0.0008	0.1545 $\pm$ 0.0011
	Dropout	22.6094 $\pm$ 0.0779	0.7552 $\pm$ 0.0001	0.1699 $\pm$ 0.0009	17.8212 $\pm$ 0.1534	0.0308 $\pm$ 0.0002	0.0188 $\pm$ 0.0001
	Normal	23.9819 $\pm$ 0.0770	0.8146 $\pm$ 0.0013	0.1058 $\pm$ 0.0021	4.9525 $\pm$ 0.7433	0.0227 $\pm$ 0.0006	0.0152 $\pm$ 0.0003
Android	MoL	22.1825 $\pm$ 0.0186	0.7395 $\pm$ 0.0002	0.1905 $\pm$ 0.0008	-0.7117 $\pm$ 0.0656	0.0273 $\pm$ 0.0006	0.0172 $\pm$ 0.0005
	Ensembles	23.4866 $\pm$ 0.0304	0.8012 $\pm$ 0.0006	0.1381 $\pm$ 0.0006	8.1690 $\pm$ 0.8485	0.0265 $\pm$ 0.0001	0.0158 $\pm$ 0.0000
	DANE	23.4866 $\pm$ 0.0304	0.8012 $\pm$ 0.0006	0.1381 $\pm$ 0.0006	7.4801 $\pm$ 0.8655	0.0274 $\pm$ 0.0001	0.0164 $\pm$ 0.0000

Table 7: Mean and standard deviation of quantitative metrics over three runs on RobustNeRF.

Figure 11: Qualitative comparison on LF.

Figure 12: Qualitative comparison on LLFF.

Figure 13: Qualitative comparison on RobustNeRF.

Figure 14: Aleatoric and epistemic uncertainty maps for three in-the-wild scenes from Phototourism. Aleatoric uncertainty peaks in regions with high radiance variance (e.g., sky higher above, building facades, moving figures), whereas epistemic uncertainty is concentrated in areas frequently occluded (e.g., sky directly behind the buildings or objects obscured by pedestrians).

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VCURF: Virtual Camera-based Uncertainty of Radiance Fields

Liyan Chen, Nathaniel Burgdorfer, Philippos Mordohai

Stevens Institute of Technology

Uncertainty Quantification Neural Rendering Neural Radiance Fields

Open paper AskPDF arXiv

Radiance fields, implemented with either implicit (NeRF) or explicit (Gaussian Splatting) representations, are advancing the state of the art in novel view synthesis at a rapid pace. Even though the rendered views they generate are often compelling, they are not free of errors. In this paper, we propose a new approach for pixel-wise uncertainty quantification based on measuring the inconsistencies among renderings by the radiance field model in virtual cameras sampled near the target viewpoint. We named our approach VCURF for Virtual Camera-based Uncertainty of Radiance Fields. VCURF treats the radiance field model as a black box, only assuming that it is capable of rendering color and depth on demand. This property makes our approach applicable to both NeRF and GS models without any modification. Our experiments on a combination of datasets, radiance field models and baselines demonstrate VCURF's effectiveness in pixel-wise uncertainty estimation. We conclude the paper with findings that question the way view selection is tackled by the majority of the current literature.

Abstract

UQ for 3D Reconstruction

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