U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching
Authors: Junsheng Zhou
XingYu Shi
Haichuan Song
Yi Fang
Yu-Shen Liu
Zhizhong Han
Venue: NeurIPS 2025 poster ()
Keywords: Unsupervised point cloud denoising
noise-to-noise matching
denoising consistency
Primary area: applications

Abstract: Point clouds captured by scanning sensors are often perturbed by noise, which have a highly negative impact on downstream tasks (e.g. surface reconstruction and shape understanding). Previous works mostly focus on training neural networks with noisy-clean point cloud pairs for learning denoising priors, which requires extensively manual efforts. In this work, we introduce U-CAN, an Unsupervised framework for point cloud denoising with Consistency-Aware Noise2Noise matching. Specifically, we leverage a neural network to infer a multi-step denoising path for each point of a shape or scene with a noise to noise matching schema. We achieve this by a novel loss which enables statistical reasoning on multiple noisy point cloud observations. We further introduce a novel constraint on the denoised geometry consistency for learning consistency-aware denoising patterns. We justify that the proposed constraint is a general term which is not limited to 3D domain and can also contribute to the area of 2D image denoising. Our evaluations under the widely used benchmarks in point cloud denoising, upsampling and image denoising show significant improvement over the state-of-the-art unsupervised methods, where U-CAN also produces comparable results with the supervised methods. Project page: https://gloriasze.github.io/U-CAN/.

U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching
Junsheng Zhou Xingyu Shi! Haichuan Song2t
Yi Fang
Yu-Shen Liu
Zhizhong Han
School of Software, Tsinghua University, Beijing, China
Computer Science and Technology, East China Normal University, Shanghai, China" Center for Al and Robotics (CAIR), NYU Abu Dhabi, UAE Department of Computer Science, Wayne State University, Detroit, USA*
(zhou-js24) (ahou-js24,shixy220 shixy22) @mails..a....mmmmmm.ammmaammalm. tsinghua. edw.. en yfangonyu. edu edu linyushen@tsinghua.ede edu.
hcaongdca edu.
h312h@wayne edu
Abstract
Point clouds captured by scanning sensors are often perturbed by noise, which have a highly negative impact on downstream tasks (e.g. surface reconstruction and shape understanding). Previous works mostly focus training neural networks with noisy-clean point cloud pairs for learning denoising priors, which requires extensively manual efforts. In this work, we introduce U-CAN, Unsupervised framework for point cloud denoising with Consistency-Awart Noise2Noise match- ing. Specifically, we leverage neural network infer a multi-step denoising path for each point of shape or scene with noise to noise matching scheme. We achieve this by novel loss which enables statistical reasoning on multiple noisy point cloud observations. We further introduce novel constraint on the denoised geometry consistency for learning consistency-aware denoising patterns. We justify that the proposed constraint is general term which is not limited to 3D domain and can also contribute to the area of 2D image denoising. Our evaluations under the widely used benchmarks in point cloud denoising, upsampling and image denoising show significant improvement over the state-of-the-at unsupervised methods, where U-CAN also produces comparable results with the supervised methods. Project page: https: //gl://loooo //llorggssea github. 1o/U-CAN/.
Introduction
3D point clouds have been fundamental representation in 3D computer vision and play key role in autonomous driving [13], augmented/virtual reality [56] and robotics [10]. While in these real world applications, the point clouds captured with scanning sensors (c.g. LiDAR) contain unavoidable noise, which leads to large errors in 3D perception and understanding. Recent learning baaninng-based approaches [27, 26, 7] have shown convincing results in denoising point clouds with neural networks by learning denoising patterns with noisy-clean point cloud pairs. However, they are limited in the amount of clean 3D geometries which require manual efforts of human 3D CAD modelling.
A straightforward observation is that despite the limited clean models, the amount of real-captured noisy point clouds is growing rapidly everyday with the LiDARs in self-driving level digital devices in our daily life, such as iPhone. Consequently, it is desirable to learn denoising patterns by solely using the noisy data itself. The subsequent approaches, such as TotalDenoising [12], therefore turn to explore unsupervised point cloud denoising by leveraging a spatial prior term
consumer
Equual contribution. |Coresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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for total-level denoisiin. However, the current unsupervised approaches still struggle to predict precise clean point cloud while keeping high-fidelity local geometries due the lack of sufficient constraints at local-level.
To solve these issues, introduce U-CAN, an unsupervised learning framework for point cloud denoising with consistency-awas noise to noise matching, Instead of predicting total-level denois- ing, we leverage neural network to infer a multi-step denoising path for each point of a shape or scene with a point-wise noise to noise matching scheme. Specifically, we learn a mapping from one noisy point cloud to another with a novel loss function which enables point-to-poin matching for investigating denoising patterns from only noisy point clouds. The key idea of this noise to noise matching leverage the statistical reasoning to reveal the clean structures upon its several noisy observations.
Another challenge in predicting robust denoising arises from the unknown location of true surfaces when only noisy observations are available. This ambiguity can lead to unstable convergence due to inconsistencies in denoising results across different noisy observations. In response this challenge, we introduce a novel consistency-aware constraint that specifically targets the denoising geometric consistency. We achieve this by minimizing the geometric differences from the denoising prediction of one noisy observation to the prediction of another. Furthermore, we demonstrate that the proposed consistency-awant denoising constraint not limited to the 3D domain, which can also significantly contribute to the field of 2D image denoising. Extensive experiments demonstrate that the proposed U-CAN outperforms stute-of-hhe-- methods in unsupervised point cloud denoising, upsampling and image denoising, where U-CAN even achieves comparable performances with the supervised methods. Our main contributions can be summarized as follows.
We introduce U-CAN, a novel framework for unsupervised point cloud denoising by design- ing neural network to infer a multi-step denoising path for each point of a noisy observation with a novel noise to noise matching loss.
a We propose a general constraint on the denoising geometric consistency across different denoising predictions, which significantly improves the denoising performance in both 3D and 2D domain.
We achieve state-of-the- -ft results in unsupervised denoising for both point clouds and images under widely used benchmarks, while also delivering performance comparable to supervised methods. U-CAN is also capable of unsupervised point upsampling through denoising.
2 Related Work
2.1 Traditional Point Cloud Denoising
Point cloud denoising plays a key role in robust 3D understanding, the point clouds captured by scanners often contain unavoidable noise. Traditional methods for optimizing noisy point clouds include local surface fitting [1, 14], sparse representation [3, 44), and graph filtering 55), all of which use geometric priors for denoising. Local surface fitting methods, such as the widely used moving least squares (MLS) method [2] and its robust extensions [35, 9], approximate the point cloud with a smooth surface using simple function approximators and project the points onto this newly formed surface for denoising. Other techniques, like jet fitting [5] and the parameterization-free local projector operator (LOP) [25, 14], have also been developed for point cloud denoising. Sparsity- based methods [3, 44] address denoising by initially predicting surface normals through optimization problems with sparse constraints.
braph methods [41, 55] represent point clouds using graphs and use graph filters for denoising. The graph-based methods are sensitive to the noise distributions due to the potential instability in graph construction.
2.2 Saaningg-assed Point Cloud Denoising
The deep learning based approaches for 3D point cloud [46, 67, 74, 49, 18, 64, 16, 73, 75, 57, 62] have largely advanced point cloud processing tasks, such as upsampling [51,24], surface reconstruc- tion [71, 72, 4, 42, 29, 65, 11, 70, 15, 69, 34, 61], consolidation [33, 52], normal estimation [23, 63), generation [76, 68, 77, 48, 66] and denoising [40, 36, 27, 26, 19, 31, 58, 47, 60]. With the emergence

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(a) F ramework
Denoise Network (Step
Denoise Network (Step 2)
Denoise Network (Sepp
Feabure Extractor
Path Predictor
(b) L Lerning Schema
Denoising Consistency
Denaise Network
Denoise Network
Nais Observeion
Naiey Charaaion B
Noise to Noise Matching
Noise to Noise Matching
Figure I: Overview of our method. (a) We design multi-step denoising framework to gradually filter the noisy point cloud. (b) We introduce a novel learning schema for unsupervised learning of point cloud denoising by proposing two constraints, i.e., Noise Noise Matching loss and Denoising Consistency loss.
of neural networks for point cloud processing, such PointNet [37], PointNet++ [38] and DGCNN [46], Icarning representations on point sets for denoising has achieved convincing performances. PointClcanNet [40] is the pioneer of lcarning-based point denoising which introduces neural net- work based on the PointNet model [37, 38J. PointFilter [59] advances PointCleanNet with a special designed filter modeling. The following work GPDNet [36] introduces graph convolutional networks for improving and stabilizing denoising process, introducing the strong capability of graph networks in handling complex geometric data the point cloud denoising task. DMRDenoise [26] introduces a new perspective for denoising by adopting an innovative downsample-upsanpll framework. More recently, ScoreDenoise [27] attempts to estimate the gradient field around each point and iteratively update the position of each point. IterativeFPNN [7] simulates a real iterative filtering process internally reduce noise.
2.3 Unsupervised Point Cloud Denoising
Previous learning-based approaches merely focus on learning denoising patterns with noisy-clean point cloud pairs and are limited in the amount of clean 3D shapes which require manual efforts of human CAD modeling. TotalDenoising [12] is the most relevant work of ours which explores unsupervised point denoising by leveraging spatial prior term for total-level denoising. However, struggles to predict precise predictions with high-fidelity local geometries. The reason is that TotalDenoising only involves the global constraint and lacks the local-level constraint which plays the key role in producing detailed predictions. DMRDenoise [26] and ScoreDenois [27] also provide an unsupervised version by introducing the total rotal-denoising loss, but both of them face the same problem as TotalDenoising [12]. A recent work [28] introduces an unsupervised approach to over-fit fit each noisy point cloud for learning signed distance functions, where each point cloud takes about more than 10 minutes to converge. We focus on the learning-based point cloud denoising which enables a fast inference.
Different from these works, we learn a data-driven matching from one noisy point cloud to another with novel loss function which enables point-to-pont matching local-level. This brings high- fidelity denoising results. We further introduce denoising consistency constraint for consistency- predictions with improved accuracy.
Architecture of U-CAN
Problem Statement. We design a neural network with novel learning schema for unsupervised point cloud denoising. Current methods train neural networks to denoise point cloud by matching with its paired clean point cloud. Different from these supervised methods, we do not require any clean point clouds as supervision, and learn to filter noisy observation Pa of 3D shape or scene S with only other several noisy observation Pa of S.
3

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Overview. The overview of proposed U-CAN is shown in Fig. 1. We will start from our denoise network Sec. 3.1 and introduce the noise noise mapping schema with novel point-wise matching loss in Sec. 3.2. We then present novel constraint on denoising consistency in Sec. 3.3 and transfer to enhance the unsupervised image denoising task Sec. 3.4.
3.1 Denoise Network
Given a noisy point cloud Pa as input, we design a multi-step denoising framework to gradually filter Pa for achieving cleaned point cloud Ca. As illustrated in Fig. 1 (a), the Denoise Network each step consists of a Feature Extractor and a Puth Predictor. We implement the Feature Extructor as series of dynamic EdgeConv from DGCNN [46] with residual connections for achieving robust representations, while the Path Predictor is composed with several linear layers to predict the moving path for each point from the extracted features.
During the i-th step of the denoising process, the Denoise Network fi takes the filtered point clouds Ch-1 from the previous step (the noisy point cloud Pa for the initial step) input. It then predicts distinct moving path Ap; for pulling each point to attain the filtered point cloud C. at the current step as C. C--1 + Apt- The final prediction C. is obtained by moving Pa gradually, formulated
N
C. = f((aa) + + E.C.""
1=2
where N > 1 is the number of steps.
3.2 Noise to Noise Matching
The common practice for predicting the clean point cloud from its noisy observations is to train neural network with Noise to Clean Matching supervisions to minimize the distance between the predicted C, with the ground truth clean point cloud Ga, formulated
L22C D(Ca, Ga);
where D) is a distance metric, typically the Chamfer Distance.
Preview Noise2Noise. Previously, Noise2Noise [22] has been proposed for unsupervised image denoising by encouraging a denoised image resemble other noisy observations of the same image. Given the appealing results in 2D domain, it seems that we can denoise 3D point cloud unsupervisedly by simply transferring the success of Noise into 3D domain. However, the conclusion of Noise2Noise is built upon the one-to-one matching correspondences, as the pixels in images. The correspondences support the key assumption of Noise2Noise that the noisy values at the same pixel location of different observations are random realizations of a distribution around a clean pixel value. While the point clouds are irregular and unordered with no correspondences where naive reproduction of Noise2Noise do not work for 3D point clouds.
A balancing approach for adapting unsupervised denoising in point clouds is to design total-level loss for global denoising without specifying the correspondences like TotalDenoising [12], yet struggles to predict precise clean point cloud while keeping local geometries with only the coarse constraint. MoiseMap [28] introduces an over- wver-fitting approach to learn signed distance functions for each noisy observation with the Noise2Noise mechanism in local-level, but fails in generalizing to new observations.
One-to-One Point Correspondences. As discussed above, we justify that the key factor preventing the adaption of Noise2Noise schema 3D domain the lack of 3D correspondences. To solve this issue, we aim to build one-to-one correspondence with a specific matching for each point. Instead of manually defining the point correspondences, we explore a suitable distance metric that potentially contains the one-to-one point correspondences as the optimizing target, which satisfies the assumptions for Noise2Noise and can naturally enable the unsupervised denoising for 3D point clouds. In practice, use Earth Moving Distance (EMD) suitable implementation of D. The EMD between two point clouds and is formulated as:
DEMD Y)
min Σ -())2(
d:
ZEX

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where & is one-to-one correspondence. With the Earth Moving Distance which potentially contains the point correspondences as the distance metric, we successfully adopt the Noise2Noise schema for unsupervised point cloud denoising- Specifically, as shown in Fig. 1 (b), given two noisy observations Pa and Pa randomly selected from set of noisy observations at each epoch, we train the Denoise Network with the Noise to Noise Matching loss to push the denoised point cloud C. to be similar to another noisy point cloud Pb. and vice versa for Cs. The Noise to Noise Matching loss formulated as:
N2N PEMD((a, Pb) + DEMD (Co, P.).
With this loss, U-CAN leverages the statistical reasoning among multiple noisy observations and effectively infers clean structures.
3.3 Denoising Consistency Constraint
Another issue that none of the previ- ous unsupervised denoising works on 2D or 3D domains noticed is that the unsupervised noise to noise matching schema struggles to produce consis- tent denoising prediction with differ- ent noisy observations as input. This leads to ambiguous optimizations for the detailed geometries. For the super- vised approaches, this is not problem since each noisy imput has distinct clean point cloud as the target. While in the situation of unsupervised denois- ing, there no true surface locations provided, and only multiple noisy obser- vations are available as inputs and tar- gets, which makes hard for the neural networks to learn consistent predictions.
Error:
7,813
5.924
Ertor:
8.24
Foc Figure 2: Illustrations the effect of proposed constraint on denoising consistency. The noise errors indicate the Chamfer distance between the denoised and the clean point clouds.
wil Foc
0.1 x Epc:
Driven by this observation, propose a novel constraint on denoising consistency for learning consistency-awe denoising patterns. Specif- ically, we push the denoised prediction of one noisy observation to be consistent with the denoised prediction of another noisy observation with a special designed loss, formulated as:
LDC DDMD Cb),
where C. and C. are the denoised predictions achieved by Eq. (1), respectively. With the simple but effective term, U-CAN is able to produce more consistent-aware predictions and further improve the denoising results at detailed local geometries.
We provide an illustration as shown in Fig. 2 to show the advantage of our pro- posed constraint LDc- We train U-CAN for learning point cloud denoising with- out LDC and show the result as "w/o LDC". We than visualize the denoising predictions of U-CAN trained with low coefficient (i.e. 0.1x) and high coeffi cient (i.e. 1x) of EDC. shown as "0.1 x LDC " and "I LDC". The comparisons demonstrate the effectiveness of LDC where better performances are achieved with larger coefficient of LDC-
Ag
Au+Dz
2
Dovise Networi
Danoised Prediction (A+D)
A
8
A2
As-D; 2
A++D.
Dezaking Curidaay
G
D
C2
D2
Noise Naise
Ag
Bg
A
B,+C 2
RynC
Network
Danoised
C3
Dg
C.
D4
Prediction (B+C)
B,+0g
B,+G,
2
Figure 3: Transferring the denoising consistency constraint
U-CAN to the unsupervised image denoising.
5

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Table 1:
Denoising comparisons under PUNet dataset. CDx 10 and P2M x x10*. The best results under the unsupervised (Un-Sup) point cloud denoising setting are highlighted.
Point Number
(SpaSe)s
50K(Dense)
Noise
1%
2%
3%
1%
2%
3%
Model
CD
P2M
CD
P2M
C1)
P2M
CD
P2M
CD
P2M
CD
P2M
Classic
Bilateral [8]
3.646
1.342
5.007
2.018
6.998
3.557
0.877
0.234
2.376
1.389
6,304
4.730
Jct [S]
2.712
0.613
4.155
1.347
6.262
2.921
0.851
0.207
2.432
1.403
5.788
4.267
MRPCA [32]
2.972
0.922
3,728
1.117
5.009
1,963
0.669
0.099
2.008
1.003
5.775
4,081
GLR [55]
2.959
1.052
3.773
1.306
4,909
2.114
0.696
0.161
1.587
0.830
3.839
2.707
Supervised
PCNet [40]
3.515
1.148
7.469
3,965
13.067
8.737
1.049
0.346
1.447
0.608
2.289
1.285
GPDNet [36]
3.780
1.337
8.007
4,426
13.482
9.114
1.113
1.037
5.021
3.736
9.705
7.998
DMR [26]
4,482
1.722
4,982
2.115
5.892
2.846
1.162
0.469
1.566
0.800
2.632
1.528
ScoreDe [27]
2.521
0.463
3.686
1.074
4.708
1.942
0.716
0.150
1.288
0.566
1.928
1.041
TTD [12]
3,390
0.826
7.251
3,485
13.385
8.740
1.024
0,314
2.722
1.567
7.474
5.729
Un-Sup
DMR-TTD
7,897
5.026
9.257
6.119
10.946
7.569
2.137
1.567
3.223
2,498
5.572
4.669
Scorel DTD
3.107
0.888
4.675
1.829
7.225
3.726
0.918
0.265
2.439
1.411
5.303
3.841
Ours
2.497
1.105
3.234
1.255
3.666
1.842
0.835
0.609
0.975
0.675
2.479
1.863
Supervised
Unsupervised
Input
PCN DMR
SconDennise
TTD
DMR-TTD
OuiS
Figure 4: Visual comparisons under PUNet dataset. The noise errors at each point is shown in color, where the points closer to the ground truth surface are represented with bluer color, indicating lower error And those with higher error are represented with redder color.
3.4 Transferring U-CAN to Image Denoising
We further justify that the observation in Sec. 3.3 is not limited in the unsupervised point cloud denoising, but is a common issue that also occurs in the unsupervised image denoising task. Therefore, we believe the proposed constraint for denoising consistency in Eq. (5) can also contribute the area of 2D image denoising. We demonstrate the effectiveness of LDC by adapting it to the state-of-the-art work ZS-N2N [30] unsupervised image denoise.
The overview modified ZS-N2N shown in Fig. 3. ZS-N2N separates an image into two downsampled sub-images and treats them two noisy observations learn residual-bascl noise to noise matching for image denoising. We further introduce our proposed constraint on denoising consistency to Z.SN2NN by minimizing the differences between one denoised sub-image and the other denoised sub-image.
4 Experiments
4.1 Point Cloud Denoising on Synthetic Data
Dataset and Metrics. For the experiments on synthetic shapes, we follow ScoreDenoise [27] to train our network on the PUNet [53] dataset. We split the dataset into training and testing sets with the same setting ScoreDenoise [27]. Poisson disk sampling algorithm used to sample point clouds from

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Noisy Points
Denoised Points by U-CAN
Noisy Points
PCN
TTD
SooceDenosse TTD
U-CAN (Ours)
Figure 5: Denoising on the real scans under Paris-rueMaadne dataset. Top: The visualization of the noisy points and denoised points obtained by U-CAN under the whole scene. Bottom: The visual comparison with the supervised and unsupervised approaches on the local scene geometries.
the meshes at two resolutions: 10k and 50k points and the Gaussian noise is subsequently introduced three different levels of standard deviations, i.e., 1 1, 2% and 3% of the bounding sphere's s radius. Following previous works PCNet [40] and DMR [26], we split point clouds into patches before being fed into the model, where the patch size set to IK. We evaluate the performance of U-CAN and
other baselines under the commonly used metrics L2 Chamfer distance (CD) and the point-to-mesh distance (P2M), following previous methods [27, 26]
Comparisons. We quantitatively compare the proposed U-CAN with the state-of-the-ar methods for both supervised and unsupervised point cloud denoising in Tab. 1. This includes classic optimization- based methods such as Bilateral [8], Jet [5], MRPCA [32]. GLR [55]: supervised learning-bas based
methods like PCNet [40], GPDNet [36], DMR [26), ScoreDenoise [27], and PointFilter [59]; and
unsupervised methods including TTD [12], as well as unsupervised adaptations of DMR [26) and ScoreDenoise [27] with the TTD loss, shown 'DMR-TTD' and 'ScoreDeenoise-TDD:
The comparative analysis of methods using synthetic data is presented in Tab. and illustrated in Fig. 4. Traditional aptimization-baan point cloud denoising methods rely heavily geometric priors to inform their smoothing algorithms and show increased sensitivity to noises with unseen variances, leading to degradation in denoising performance. For unsupervised denoising, the TTD [12] fails to produce high-fidelity local geometries with only the global constraints. The unsupervised versions of DMR [26] and ScoreDenoise [27] which leverage the same constraint TTD, share same limitations of TTD and presents sub-optimal performance at both low and high resolutions due to the lack of local-level constraints.
As presented, our model significantly outperforms previous unsupervised denoising methods, espe- cially for noises with large variances, and can even rival the results of supervised methods in the majority of cases. In particular, at the 10K resolution and under noise levels of 2% and 3%, our method outperforms all other supervised and unsupervised methods in the evaluation.
We provide the visual comparison among the state-of-the-an -fr supervised and unsupervised point cloud denoising methods in Fig. 4. The error at each point in the point cloud is depicted in color. Points that are closer to the ground truth surface are shown in blue, indicating lower error, while those with higher error are shown in red. As shown in the figure, our results produces significantly more -ppeelinp denoising results compared to other unsupervised approaches and even some supervised ones.
7

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20.06 dB
25.04 dB
26.49
28.13
29.14
20.13 dR
25. dis
26. di
27.51
dis
Noiey
DIP
BM3D
ZN-N2N
Ours
GT
Figure 6: Visual comparison of unsupervised image denoising under McMaster18 18 dataset.
4.2 Point Cloud Denoising on Scanned Data
For demonstrating the capability of U-CAN to handle real-world point cloud noises, we conduct evaluations under the Mardaee dataset [43] which is obtained from real world using laser scanners. We directly leverage the U-CAN model trained on PUNet dataset for evaluating, without requiring extra training. The visualization of denoised scene point cloud is shown in Fig. 5. Since the ground truth point cloud is not available, our evaluations are primarily qualitative, focusing on visual assessments rather than quantitative metrics.
As shown in Fig. 5, U-CAN preserves the intricate details better and yields a cleaner and smoother surface. On the scene in the top row, our method demonstrates marked improvement over the other compared methods, particularly around complex structures like trees and cars. In the bottom row, we observe that windows are denoised with greater clarity and cleanliness with the proposed U-CAN. We also produce accurate denoising results of the surrounding structures such as the walls and vehicles.
4.3 Evaluatioins in Image Denoising
Dataset and Metrics. We further evaluate the proposed denoising consistency constraint for improv- ing the image denoising qualities. For evaluating in the image denoising task, we follow ZS-N2N [30] to conduct experiments under the McMaster1 8 dataset [20]. Our evaluation setting keeps the same ZS-N2N, and center-crop the images into patches of size 256 256. We examine under poisson noise with noise levels À = 10, 25, 50. We leverage the commonly-used PSNR in dB as the evaluation metric.
We compare the proposed image denoising adaption of U-CAN with the state-of- the-art methods for unsupervised image denois- ing, including the dataset-based Noise2Clean (N2C). Neighbour2eeihhbour (NB2NB) [17], Noise2 (N2V) [21], and the dataset free methods BM3D [6], DIP [45], Self2Self (S2S) [39] and 7S-N2N [30]. We show the quanti- tative comparison in Tab. 2, where the denois- ing consistency constraint demonstrates superior performance compared to the previous methods. Specifically, by introducing the proposed de- noising consistency constraint into ZS-N2N, we achieve significant improvements nearly 1 dB over the baseline ZS-N2N, The visual compar- ison is shown Fig. The denoised images of U-CAN are more accurate and with more details than previous state-of-the-art methods. This particularly clear in areas high-frequency information, such as edges, textures, and intricate patterns, where our method maintains the integrity of these details while effectively reducing noise.
Comparisons.
Table 2: Unsupervised image denoising under Mc- Master18 dataset. The PSNR scores in dB are reported. Best results marked in bold and the second-best results are underlined.
Noise
Method
McMaster18
known?
50
26
10
dataset- t-bss-ddddd
N2C
yes
29.89
28:20
26.42
D0
28 62
27.51
NB2NB
yes
29.41
27.79
25.95
Poisson
D0
28.03
27.66
N2V
yes
27.80 86
25.65
23.47
26.34
25.52
datesct-rre
BM3D
D0
27.33
24.77
21.59
DIP
28.73
27.37
S28
27.55
27.24
26.39
ZS-N2N
30.36
28.41
25.75
Ours
31.03
29.14
26.52

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#Points
5K
10K
CD
P2M
CD
P2M
PU-Net [53]
3.445
1.669
2.862
1.166
ScoreDenoise [27]
1.696
0.295
1,454
0.181
DMR-TTD 126, 12]
5.846
4.045
4.710
3.833
ScoreD-TTD [27, 12]
3.286
1.889
2.403
1.683
Ours
1.532
0.585
1.212
0.587
Spane
Table 3: Point cloud upsampling results under PU- Net dataset.
Figure 7: Visual Comparison under PU-Net.
4.4 Point Upsampling via Denoising
Implementation. We further justify that the proposed U-CAN is applicable in point cloud upsampling task, without requiring sparse-dense point cloud pairs and even without requiring the clean point clouds. We follow ScoreDenoise [27] to conduct experiments in the point cloud upsampling task. Specifically, given a sparse point cloud with M points as the input, we add Gaussian noise to it for r times independently, resulting in noisy dense point cloud containing rM points. We then feed the merged noisy point cloud to the trained U-CAN model get the final upsampled point cloud by predicting the denoised points.
Dataset and Metrics. We follow ScoreDenoise [27] to conduct the point cloud upsampling exper- iments under the PU-Net dataset. We report the evaluation metrics chamfer distance (CD) and point-to-mesh (P2M).
Comparisons. We compare our proposed U-CAN with the classical updsampling network PU-Net [53]. We further apply the adaption from denoising to upsampling to the state-of-the-ar unsupervised point cloud denoising methods DMR-ITU and ScoreDenoise-T TTD and report their upsampling per- formances. The quantitative results are shown in Tab. 3, where our method significantly outperforms DMR-TTD and ScoreDenoise- TTD, and also achieve better performance than the supervised method PU-Net designed for the upsampling task. Note that U-CAN does not require (1) sparse-to-dense point cloud pairs and (2) clean point clouds, where the only required data is the noise point clouds themselves. We further provide the visual comparison of point cloud upsampling with previous state-of-the-art unsupervised denoising methods in Fig. 7
4.5 Ablation Studies
Noise-to-Noise Matching Loss LNNN. We investigate the role of EMD-based one-to-one point correspondences in LNNN. As shown in Tab. 4, replacing EMD with CD leads to suboptimal patterns, while using Density-aware Chamfer Distance (DCD) [50] causes severe divergence. These results highlight the necessity of one-to-one matching for effective unsupervised denoising.
Denoising Consistency Loss LDc. To justify the effectiveness of constraint LDc, we remove it and vary the underlying distance metric. Without LDC, performance significantly drops (e.g., CD
Table Ablation studies on the framework and loss designs.
Table 5: Ablation studies on step numbers in the denoise network.
Dutaset: PU
10K,
1%
10K,
10K,
3%
Dataset: PU
10K. 1%
10K. 2%
10K,
Exex
Loc
CD
P2M
CD
P2M
CD
P2M
Ablation
CD
CD
P2M
CD
P2M
CD
EMD
15.48
11.36
17:12
13.22
21.39
17.01
1 step
2.676
1.046
3,903
1.700
5.251
2.720
EMD
booken
steps
2.069
EMD
EMD
2.497
1.105
3.234
1.255
3.666
1.842
3 steps
2.492
1.096
3.246
1.554
3.704
1.878
X
0.725
steps
2.497
1.105
3.234
1.255
3.666
1.842
EMD
CD
2.108
0.650
3.717
1.633
7,230
4,469
steps
1.151
3.746
1.903
FMD
ICD
2,036
0.608
3.358
1.367
6.847
4.144
6 stops 7 steps
2,509
1.107
3.225
1.235
3.753
1.857
EMD
RMD
2.497
1.105
3.234
1.255
3.666
1.842
2.470
1.080
3.321
1.243
3.785
1.866

---

increases from 3.66 to 7.22 under '10K. 3%"), indicating its critical role in enforcing consistent predictions across noisy inputs. EMD again proves to be the most effective metric.
Number of Denoising Steps. We study the impact of varying the number of denoising steps N from 1 to 7. As shown in Tab. 5, performance improves up N=4, beyond which gains saturate or slightly degrade. Thus, 4 steps offer good trade-off between accuracy and efficiency.
5 Conclusion
In this work, we introduce U-CAN, an Unsupervised framework for point cloud denoising with Consistency-Awan Noise2Noise matching. We train a neural network to infer denoising path for each point of shape with noise to noise matching scheme. Our novel loss enables statistical reasoning on noisy point cloud observations. We also introduce a novel constraint on the denoising geometry consistency for learning consistency-awart denoising patterns. Our evaluation for point cloud denoising and image denoising demonstrates that even without clean supervision, U-CAN also produces comparable denoising results with the state-of-the-arr supervised methods.
6
Acknowledgement
This work was supported by Deep Earth Probe and Mineral Resources Exploration National Science and Technology Major Project (2024ZD1033405), and the National Natural Science Foundation of China (62272263), and in part by Kuaishou. Junsheng Zhou is also partially funded by Baidu Scholarship.
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Reviews:
[{"review_id": "lzR26G98Yd", "reviewer": "Reviewer_gzhj", "summary": "This paper introduces U-CAN, a novel unsupervised framework for denoising 3D point clouds without needing clean reference data. [24] The method trains a neural network using a \"Noise-to-Noise\" matching scheme, where the goal is to make the denoised version of one noisy point cloud resemble another noisy observation of the same object. [25, 54] Key to its success is a new loss function based on Earth Moving Distance (EMD) to establish point correspondences, and a \"Denoising Consistency\" constraint that ensures predictions from different noisy inputs remain consistent. The authors demonstrate that U-CAN significantly outperforms state-of-the-art unsupervised methods and achieves comparable results to supervised techniques in point cloud denoising, upsampling, and even 2D image denoising.", "questions": "- The choice of Earth Mover's Distance (EMD) is well-justified by its ability to find one-to-one correspondences, which is critical for the Noise-to-Noise matching loss. However, EMD is known to be computationally expensive. Can you give a rough number on the computational and training time of the denoise model.\n\n- Can you clarify how are different noisy observations P_a and P_b generated? \n\n- Since U-CAN performs an 1-1 matching between noisy and denoised point clouds (PC), I am curious how are the noisy points mapped to the denoised ones. Would the cluster of noisy points mapped into their closest point from the denoised PC?", "limitations": "See the questions.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strength:**\n- The work introduces U-CAN, an innovative unsupervised framework that learns to denoise point clouds without requiring pairs of noisy and clean data, which are often difficult and expensive to create.\n\n- The core concept of denoising consistency is shown to be a general principle that can be transferred to improve unsupervised 2D image denoising as well.\n\n- The paper is well presented with solid experiment results.", "was_revised": false, "final_justification": "", "rebuttal": "We deeply appreciate the reviewer gzhj for the thoughtful feedback and time invested in evaluating our work. We respond to each question below.\n\n**Q1: The computational cost and training time of U-CAN.**\n\nAs the reviewer correctly pointed out, the computational cost of EMD increases substantially with the number of points. We address this problem by learning point denoising at the patch level, where EMD is computed only between local point cloud patches containing a relatively small number of points (around 1,000). This strategy significantly reduces training cost and leads to more robust and efficient denoising. We conducted an ablation study to investigate the impact of varying patch sizes at Sec.D and Table 11 of the Appendix, where the results indicate that a patch size of 1,000 points is optimal for U-CAN. This configuration supports efficient training with EMD, where the convergence of U-CAN takes only about 25 hours on a single NVIDIA 3090 GPU. For reference, the training of ScoreD-TTD takes about 40 hours on a single NVIDIA 3090 GPU. \n\nFor the reviewer’s convenience, we include Table 11 from the Appendix below.\n\n***Table 11 of the Appendix: Ablation studies on point cloud patch sizes.***\n\n| Dataset: PU |          |   10K, 1%   |         |   10K, 2%   |         |   10K, 3%   |         |\n|-------------|----------|-------------|---------|-------------|---------|-------------|---------|\n| Ablation    |          |     CD      |  P2M    |     CD      |  P2M    |     CD      |  P2M    |\n| 250         |          |    2.821    | 1.302   |    3.327    | 1.515   |    4.239    | 2.152   |\n| 500         |          |    2.843    | 1.432   |    3.390    | 1.703   |    3.898    | 2.004   |\n| **1000**    |          | **2.497**   |**1.105**| **3.234**   |**1.255**| **3.666**   |**1.842**|\n| 2000        |          |    2.616    | 1.175   |    3.247    | 1.547   |    3.880    | 1.994   |\n\nMoreover, we clarify that EMD is used only during training and does not affect the inference efficiency of U-CAN. Table A below presents a comparison of inference times between U-CAN, state-of-the-art unsupervised baselines (ScoreDenoise-TTD, DMR-TTD), the supervised baseline PCN, and the traditional algorithm GLR.\n\n***Table A. Runtime comparisons under PU-Net dataset.***\n\n| Method        | Time (s) |\n|---------------|----------|\n| GLR (Traditional)          | 101.20    |\n| PCN (Supervised)          | 167.75   |\n| DMR-TTD   | 11.08    |\n| ScoreDenoise-TTD  | 18.70     |\n| **Ours**      | **10.90**     |\n\n**Q2: How are different noisy observations generated.**\n\nThe noisy observations $P_a$ and $P_b$ can be achieve by: a) multiple noisy observations of the same object. The manner is supported by modern LiDAR systems which can capture multiple (10-30) noisy observations per second. b) several subsets of a dense noisy observation. For example, we can achieve 5 training instances of 10k points from a noisy observation of 50k points. An ablation study of training U-CAN with these two input patterns can be found on Table 12 of the Appendix, where the results demonstrate the effectiveness of both kinds of input.\n\nFor the reviewer’s convenience, we include Table 12 from the Appendix below.\n\n***Table 12 of the Appendix: Ablation studies on input patterns.***\n\n| Dataset: PU         |          | 10K, 1%   |         | 10K, 2%   |         | 10K, 3%   |         |\n|---------------------|----------|----------|---------|----------|---------|----------|---------|\n| Ablation            |          | CD       | P2M     | CD       | P2M     | CD       | P2M     |\n| Multiple 𝒫          |          | **2.497** | **1.105** | **3.234** | **1.255** | 3.666 | **1.842** |\n| Subsets of One 𝒫    |          | 2.580    | 1.231   | 3.287    | 1.661   | **3.605** | 1.869   |\n\n**Q3: The 1-1 matching pattern between noisy and denoised point clouds.**\n\nYes, your understanding is correct: clusters of noisy points $P_a$ are mapped to their \"closest\" points in the denoised point cloud of another noisy observation $P_b$, based on Earth Mover's Distance (EMD). It is important to note that \"closest\" here is defined by EMD, which seeks to minimize the total one-to-one transport cost from $P_a$ to the denoised $P_b$, rather than the point-wise Euclidean distance. Mapping based on Euclidean distance is consistent with the implementation of Chamfer Distance, which has been shown to fail to converge under the noise-to-noise matching scheme in unsupervised point cloud denoising, leading to a severe degradation of CD/P2M from 2.497/1.105 to 15.14/11.36, as demonstrated in Table 4 of the ablation study.\n\nThe core insight of the noise-to-noise matching scheme is that, by aligning one noisy observation with the denoised prediction of another observation of the same shape in a one-to-one manner, the underlying clean structure can be statistically inferred.\nHowever, we also observe that this strategy may result in inconsistencies across different denoising results. To address this, we propose a consistency-aware constraint that minimizes geometric differences between pairs of denoised predictions, leading to more robust denoising performance."}, {"review_id": "yUFFBVptf4", "reviewer": "Reviewer_25Zo", "summary": "This paper extends Noise2Noise in the field of 2D image denoising to 3D data, and achieves high-quality point cloud denoising through the proposed \"Noise to Noise Matching\" and \"Denoising Consistency Constraint\".", "questions": "1. This experiment adds various noises to the clean PUNet dataset to synthesize network inputs. I wonder if the noise distributions of Pa and Pb are consistent. In other words, are Pa and Pb obtained by adding the same level of noise to the same clean shape/scene, but with different noise distributions?\n2. If the noise distributions of Pa and Pb are different, I believe there is a risk of data leakage. Since Pa and Pb are contaminated with noise in different areas, the network could directly learn from the complementary regions of Pa and Pb without any denoising.\n3. I also noticed that the authors added real-world noise to PUNet for their experiments. I would like to know how U-CAN performs in denoising single-frame point clouds that contain noise in the real world.\n4 . This work contains two branches, Pa->Ca and Pb->Cb. I am curious whether the networks of these two branches are two independent networks or the same network with shared weights? Compared with existing unsupervised algorithms, does U-CAN have an advantage in model complexity?\n5. U-CAN contains two parallel denoising branches. Does this greatly increase the inference time of the model? I hope the author can provide relevant data.", "limitations": "The core idea of this work comes from Noise2Noise for 2D image denoising, but I didn't see any relevant content in the introduction of the manuscript.\nThe latest comparison algorithm in this work is from 2021, which makes it difficult to explain the superiority of U-CAN.", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "The structure is clear, and the proposed U-CAN can achieve data denoising across multiple modalities with good performance.", "was_revised": true, "final_justification": "After checking the authors' response and other reviews. And I lean to keep the original rating.", "rebuttal": "We deeply appreciate the reviewer 25Zo for the thoughtful feedback and time invested in evaluating our work. We respond to each question below.\n\n**Q1: The noise distribution of different noisy observations.**\n\nThe noisy observations $P_a$ and $P_b$ are corrupted with noise sampled from the same distribution. We clarify that the training samples can be obtained in two ways: a) multiple noisy observations of the same object. This is done by adding noise drawn from the same distribution multiple times to the same object. The introduced noises are just different samples from the same noise distribution. This setting is realistic and supported by modern LiDAR systems, which can capture 10–30 noisy observations per second with a consistent noise distribution. b) several subsets of a dense noisy observation. For example, we can achieve 5 training instances of 10k points from a noisy observation of 50k points.  Since all subsets originate from the same noisy observation, they share the same noise distribution.\n\nIn conclusion, both approaches produce training data with a consistent noise distribution. An ablation study comparing these two input strategies is presented in Table 12 of the Appendix, where results demonstrate the effectiveness of both.\n\nFor the reviewer’s convenience, we include Table 12 from the Appendix below.\n\n***Table 12 of the Appendix: Ablation studies on input patterns.***\n\n| Dataset: PU         |          | 10K, 1%   |         | 10K, 2%   |         | 10K, 3%   |         |\n|---------------------|----------|----------|---------|----------|---------|----------|---------|\n| Ablation            |          | CD       | P2M     | CD       | P2M     | CD       | P2M     |\n| Multiple 𝒫          |          | **2.497** | **1.105** | **3.234** | **1.255** | 3.666 | **1.842** |\n| Subsets of One 𝒫    |          | 2.580    | 1.231   | 3.287    | 1.661   | **3.605** | 1.869   |\n\n**Q2: Can the network learn from complementary regions of $P_a$ and $P_b$?**\n\nWe would like to clarify that all regions of the training noisy observations $P_a$ and $P_b$ are corrupted with noise from the same distribution and at the same level. There are no \"complementary regions\" that could result in data leakage. Actually, we add the noises to the entire global shape, where each single point at every location of the global shape is perturbed by noise sampled from the same distribution.\n\n**Q3: The performance of U-CAN under point clouds contain noise in the real world.**\n\nWe fully recognize the importance of evaluating U-CAN on real-world scans. In fact, we have conducted experiments and demonstrated the performance of U-CAN on the Paris-rue-Madame dataset, which is an outdoor real-world dataset acquired using laser scanners and contains complex scanning noise. Please refer to Sec.4.2 of the main paper for more details on the experimental settings and visualizations. A comprehensive comparison between U-CAN and both supervised and unsupervised baselines, including PCN, DMR-TTD, and ScoreDenoise-TTD, is presented in Figure 5 of the main paper.\n\nParis-rue-Madame is a real-world **outdoor** scanned dataset. For a more comprehensive evaluation on the performance of U-CAN, we conduct another experiment on a real-world **indoor** scanned dataset ScanNet. The input data from ScanNet consists of noisy point clouds captured by scanning sensors. We apply U-CAN to denoise these scans and evaluate the results by comparing the predictions with the ground-truth clean meshes provided in the dataset. Quantitative results and comparisons with state-of-the-art unsupervised denoising methods are shown in Table B below, where U-CAN achieves the best performance.\n\n***Table B. Comparisions under indoor ScanNet dataset .***\n\n| Method        | CD | P2M |\n|---------------|----------|----------|\n| DMR-TTD   | 2.629    |   2.381  |\n| ScoreDenoise-TTD  | 2.474     | 2.524     |\n| **Ours**      | **1.798**     | **1.897**     |\n\nU-CAN achieves superior performance on both the indoor and outdoor scene point clouds scanned in the real world, demonstrating its remarkable capability in real-world downstream applications in robotics, autonomous driving, AR/VR, and indoor navigation. \n\n**Q4: The model weights in two branches of U-CAN, model complexity and inference time.**\n\nThe two branches in U-CAN are actually the same network with shared weights, and therefore do not introduce any additional model complexity. U-CAN contains *~ 789K* parameters, which is slightly more than ScoreDenoise (*~ 187K*) and DMR (*~ 225K*). However, we argue that U-CAN remains a lightweight network, as most recent (supervised) point cloud denoising methods contain over 1M parameters.\n\nWe also clarify that U-CAN achieves comparable runtime to other unsupervised point cloud denoising methods despite having more parameters, thanks to its efficient EdgeConv-based architecture. Table A below presents the inference time comparison between U-CAN, state-of-the-art unsupervised baselines (ScoreDenoise-TTD, DMR-TTD), the supervised baseline PCN, and the traditional algorithm GLR.\n\n***Table A. Runtime comparisons under PU-Net dataset.***\n\n| Method        | Time (s) |\n|---------------|----------|\n| GLR (Traditional)          | 101.20    |\n| PCN (Supervised)          | 167.75   |\n| DMR-TTD   | 11.08    |\n| ScoreDenoise-TTD  | 18.70     |\n| **Ours**      | **10.90**     |\n\n\n**Q5: The introduction of Noise2Noise.**\n\nWe thank reviewer 25Zo for the valuable suggestion to include more descriptions of Noise2Noise in the introduction. In fact, we have devote a full paragraph (L.139-L.144) on Sec.3.2 to introducing the original work and core techniques of Noise2Noise. To provide a more comprehensive background, we will add more content of Noise2Noise to the introduction. Specifically, we will add the sentense before L.34:\n\n*\"Noise2Noise [19] is a pioneering framework for unsupervised image denoising, which learns to produce clean images by encouraging the denoised output to resemble other noisy observations of the same image at pixel-level. Inspired by Noise2Noise [19], we introduce U-CAN ...\"*\n\n\n**Q6: The compared algorithms.**\n\nWe would like to clarify that most recent works focus on supervised point cloud denoising. In the area of learning-based unsupervised point cloud denoising, the compared methods DMR-TTD and ScoreDenoise-TTD are the most recent and relevant to U-CAN. Additionally, we have included a comparison with another recent overfitting-based approach, NoiseMap, published at ICML 2023, in Table 9 and Figure 9 of the Appendix. U-CAN demonstrates comparable performance to NoiseMap, both quantitatively and qualitatively.\n\nFor the reviewer’s convenience, we include Table 9 from the Appendix below.\n\n***Table 9 of the Appendix: Comparisons with over-fitting method NoiseMap.***\n\n| Method   | CD     | P2M    | Time     |\n|------------|--------|--------|----------|\n| NoiseMap [28] (ICML 2023) | 4.221  | 1.847  | 627.0 s  |\n| **Ours**   | **3.666** | **1.842** | **10.9 s** |\n\nThe reason we do not include NoiseMap in the comparison in the main paper is that it is an overfitting approach, requiring more than 10 minutes to converge for each noisy observation and failing to generalize to new observations. With redundant overfitting, NoiseMap achieves good performance but cannot be used in real world applications. Therefore, we excluded NoiseMap from Table 1, as comparing it with other learning-based baselines would not be fair. Nonetheless, U-CAN achieves comparable performance to NoiseMap, with ***60x*** faster runtime, demonstrating its robustness and superiority."}, {"review_id": "5El2VfRhY8", "reviewer": "Reviewer_y6U3", "summary": "This paper proposes an unsupervised multi-step point cloud denoising network, which leverages a noise-to-noise matching loss and a geometric consistency loss to guide training. The proposed approach achieves competitive performance in unsupervised denoising tasks.", "questions": "Please refer to the \"weakness\" section mentioned above.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**: \n- The paper is well-organized and easy to follow.\n- The topic of unsupervised point cloud denoising is meaningful.\n- Enforcing consistency among denoised results from different scans of the same object/scene is a reasonable and insightful strategy.\n\n**Weaknesses**: \\\nMajor Concerns:\n- 1. The motivation and core framework of this paper closely resemble the *Noise2NoiseMapping* approach proposed in [1]. Several key statements are similar with the phrasing of [1]. For example:\\\nline 39 of this paper: \"**The key idea** of this noise to noise matching is to leverage the **statistical reasoning** to reveal the clean structures upon its several noisy observations\" \\\nline 140: \"The correspondences support the key assumption of Noise2Noise that **the noisy values at the same pixel location of different observations are random realizations of a distribution around a clean pixel value.**\" \\\nWhile sharing similar motivations with prior work can be acceptable, the proposed solution itself also exhibits notable similarities. Both this paper and [1] achieve unsupervised denoising by ensuring that the denoised output of a noisy scan aligns closely (in terms of EMD) with other scans of the same object/scene. Notably, the use of EMD as a loss metric was presented as a contribution in [1], and has since been adopted in other works such as [2].\n- 2. The multi-step denoising design should not be claimed as a contribution (line 54), as similar multi-stage frameworks have been explored since [3]. Does the proposed multi-step denoising framework apply a loss function at each step for supervision? Prior studies have shown that applying supervision at each stage can enhance denoising performance.\n- 3. The experimental section does not include a comparison with [1], which is a highly relevant baseline.\n- 4. As shown in Table 1, the proposed method performs worse in terms of P2M under low noise levels compared to moderate or high noise. This is counterintuitive since low-noise data should be easier to denoise. Could the authors provide an explanation for this?\n\nMinor Concerns:\n- 1. The related work section misses several recent fully-supervised denoising methods proposed after [3]. Even though the paper focuses on unsupervised methods, a brief discussion of these approaches would provide better context.\n- 2. Lines 110 and 116 use the word \"schema,\" which appears to be a typo and should be corrected to \"scheme.\"\n- 3. Please clarify what the symbol P denotes in Equation (1).\n- 4. In Figure 5, the proposed method appears to over-smooth some structural details, particularly on flat surfaces such as walls. This might be a common issue in unsupervised methods, and the authors have mentioned this limitation. Still, it would be helpful to give some possible solutions.\n\n[1] Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping\\\n[2] Denoising Point Clouds in Latent Space via Graph Convolution and Invertible Neural Network\\\n[3] IterativePFN: True Iterative Point Cloud Filtering", "was_revised": true, "final_justification": "The authors have addressed most of my concerns, and I am satisfied with the additional experiments, clarifications, and overall presentation. My main reservation remains the similarity to Noise2NoiseMapping in the underlying principle, though I acknowledge the differences in learning scheme and framework, as well as the novelty of enforcing cross-scan consistency. The claimed extension to other modalities still requires stronger validation.\nOverall, while the work may not be highly groundbreaking, it contains merits and acknowledged novelty. I can raise my score to 4.", "rebuttal": "We deeply appreciate the reviewer y6U3 for the thoughtful feedback and time invested in evaluating our work. We respond to each question below.\n\n**Q1: The difference on motivation and core framework with NoiseMap.**\n\nWe would like to thank the reviewer y6U3 for pointing out the similarity in motivation between U-CAN and NoiseMap [1]. U-CAN did share a similar motivation with NoiseMap in transferring the success of the Noise2Noise scheme from the 2D image domain to 3D point cloud denoising. However, the core framework and methodology of U-CAN differ significantly from those of NoiseMap in four key aspects:\n\n**1. Learning scheme and framework.** NoiseMap is an overfitting approach which requires more than **10 minutes** to converge for each noisy observation and cannot generalize to new observations. In contrast, U-CAN is a standard learning-based point cloud denoising framework that learns data-driven patterns during training. The resulting model can directly generalize to unseen noisy observations with a fast inference time (**10 seconds**). As a result, U-CAN is suitable for downstream tasks, while NoiseMap’s reliance on per-instance overfitting hinders its use in real-world scenarios.\n\n**2. Difference in core contributions.** (a) A key innovation of U-CAN is the *Denoising Consistency Constraint*  which aims to learn consistent denoising patterns by minimizing geometric differences between the denoised outputs of different noisy observations. We are the first to identify and address an overlooked issue in prior unsupervised denoising methods for 2D and 3D domains: the Noise2Noise scheme often fails to produce consistent predictions from different noisy inputs, leading to ambiguity in optimizing fine geometric details.\n\n(b) Beyond 3D vision, another key contribution of U-CAN is its extension to unsupervised denoising in other modalities. The proposed *Denoising Consistency Constraint* is a general term applicable to both 3D point cloud and 2D image denoising. We introduce a modified version of SOTA unsupervised image denosing method ZS-N2N, achieving significant performance gains. We believe this general constraint can benefit unsupervised denoising across a broader range of modalities, including but not limited to 2D and 3D vision—for example, speech denoising.\n\n**3. Representation difference.** NoiseMap adopts Signed Distance Functions (SDFs) as its 3D shape representation, which are inherently limited to closed surfaces. In contrast, U-CAN predicts denoising paths directly on point clouds, enabling it to represent 3D shapes with arbitrary topologies. To evaluate the performance of both NoiseMap and U-CAN on non-closed 3D shapes, we conducted additional experiments on the DeepFashion3D dataset, which consists of 3D garments with open surfaces. Quantitative comparisons are presented in Table C below.\n\n***Table C: Comparisons with NoiseMap under DeepFashion3D.***\n\n| Method   | CD     | P2M    |\n|------------|--------|--------|\n| NoiseMap | 6.392  | 3.173  |\n| **Ours**   | **1.036** | **0.586** |\n\n**4. Model architecture.** The architectures of NoiseMap and U-CAN differ significantly. NoiseMap is an overfitting method that uses a simple MLP as its neural network backbone. In contrast, U-CAN is designed as a robust learning-based point cloud denoising model with efficient inference, adopting a multi-step architecture built upon dynamic EdgeConv modules.\n\n**Q2: Lack of comparison with NoiseMap.**\n\nWe would like to clarify that we have conducted comprehensive comparison between U-CAN and NoiseMap in terms of both performance and efficiency. Section C.1 of the Appendix is dedicated to this comparison: Table 9 reports quantitative results on CD, P2M, and runtime, while Figure 9 provides visual comparisons. These results demonstrate that U-CAN achieves performance comparable to NoiseMap, both quantitatively and qualitatively.\n\nFor the reviewer’s convenience, we include Table 9 from the Appendix below.\n\n***Table 9 of the Appendix: Comparisons with overfitting method NoiseMap.***\n\n| Method   | CD     | P2M    | Time     |\n|------------|--------|--------|----------|\n| NoiseMap [28] | 4.221  | 1.847  | 627.0 s  |\n| **Ours**   | **3.666** | **1.842** | **10.9 s** |\n\nThe reason we do not include NoiseMap in the comparison in the main paper is that it is an overfitting approach, requiring more than 10 minutes to converge for each noisy observation and failing to generalize to new observations. With redundant overfitting, NoiseMap achieves good performance but cannot be used in real world applications. Therefore, we excluded NoiseMap from Table 1, as comparing it with other learning-based baselines would not be fair. Nonetheless, U-CAN achieves comparable performance to NoiseMap, with ***60x*** faster runtime, demonstrating its robustness and superiority.\n\n\n**Q3: Claim of multi-step denoising.**\n\nWe fully acknowledge that the multi-step denoising design was first introduced in IterativePFN and should not be claimed as a contribution. We will revise the statement in L.54 to *\"We introduce U-CAN, a novel framework for unsupervised point cloud denoising by **leveraging** a neural network to infer a multi-step denoising path ...\"*\n\n**Q4: Loss function setting of multi-step denoising.**\n\nIndeed, your understanding is accurate: the multi-step denoising framework applies a loss function at each step for supervision. We observed the same phenomenon as previous studies, where applying loss functions at each step results in more robust point cloud denoising. The results of our ablation studies on the loss settings are reported in Table D below.\n\n***Table D: Ablation studies on the multi-step loss setting.***\n\n| Dataset: PU    |   | 10K, 1%   |      | 10K, 2%   |      | 10K, 3%   |      |\n|---------------------|----------|----------|---------|----------|---------|----------|---------|\n| Ablation   |  | CD    | P2M     | CD       | P2M     | CD   | P2M     |\n| Only supervise last step    |     | 2.990    | 1.272   | 4.091    | 2.057   | 5.542 | 3.231   |\n| **Ours**   |     | **2.497** | **1.105** | **3.234** | **1.255** | **3.666** | **1.842** |\n\n**Q5: Performance under low noise levels.**\n\nWe would like to clarify that the \"worse\" P2M performance at 1% noise is actually due to a version difference in the P2M implementation used in ScoreDenoise. For direct comparison with our most relevant baseline, ScoreDenoise, we directly report the numerical results from their paper. However, the P2M implementation in PyTorch3D used by ScoreDenoise was unstable at the time of their results, leading to abnormally good outcomes that cannot be reproduced with the latest version, particularly at lower noise levels (e.g., 1%). For more details, please refer to Issue 12 in the ScoreDenoise GitHub repository. Recent supervised methods, such as IterativePFN (CVPR 2023), DP-LTS (CVPR 2024), and 3DMambaIPF (AAAI 2025), have confirmed the issue and follow the stable PyTorch3D P2M function. With this stable function, P2M values are significantly higher. Please refer to Table 1 in IterativePFN for details.\n\nWe justify that we use the same stable PyTorch3D implementation as IterativePFN/DP-LTS/3DMambaIPF, which also face the issue of larger P2M values. To ensure a fair comparison, we will update Table 1 in U-CAN with results from IterativePFN. We update the P2M results for ScoreDenoise-TTD using the stable implementation and report them in Table E below. Note that all P2M results in U-CAN, except for Table 1, are evaluated with the consistent stable PyTorch3D version and do not suffer from this issue.\n\n***Table E: Updated P2M comparison with ScoreDenoise-TTD.***\n\n| Dataset: PU| | 10K | | | 50K | |\n|------------|--------|--------|--------|--------|--------|--------|\n|    | 1%   | 2%  |3%| 1%    | 2%   |3%|\n| ScoreDenoise-TTD | 1.355  | 2.185  |  3.765  | 0.655  | 1.720 | 4.166  |\n| **Ours**   | **1.105** | **1.255** | **1.842** | **0.609** | **0.675**| **1.863**|\n\nFurthermore, we would like to clarify that U-CAN consistently outperforms previous unsupervised methods across all noise levels, including those lower than 1% and higher than 3%. We have conducted comprehensive comparisons in Section C of the Appendix, where Table 7 and Table 8 demonstrate that U-CAN significantly outperforms the unsupervised SOTA methods GLR, DMR-TTD, and ScoreDenoise-TTD at noise levels of 0.2%, 0.5%, 4%, and 5%.\n\n**Q6: Missing related works.**\n\nWe greatly thank reviewer y6U3 for the advice on improving the related work section. We follow the suggestions to include more discussions of latest full-supervised denoising methods. We will add the statements in Sec.2.2, after L.91:\n\n*\"StraightPCF advances IterativePFN by learning to move noisy points to the clean surfaces along the shortest path. PD-LTS designs an invertible network for achieving noise disentanglement in the latent space. P2PBridge and SuperPC incorporate diffusion models into point cloud denoising. 3DMambaIPF  leverages the powerful Mamba model for more efficient point denoising.\"*\n\nThe corresponding references will be added.\n\n**Q7: Over-smooth results on flat surfaces.**\n\nWe acknowledge that over-smoothing on flat surfaces (e.g., walls) is a common issue in unsupervised methods. We thank reviewer y6U3 for the insightful comment. A practical solution is to reduce the number of denoising steps, especially in scenes with rich structural details. In our observations, a small number of steps (e.g., 1 to 2) is sufficient to remove strong noise like artifacts near windows or road signs, while also preserving flat surface details. We will include visualizations on the Paris-rue-Madame dataset using the 1 to 2 step version of U-CAN in the revised submission, since figures cannot be uploaded during the rebuttal phase of NeurIPS.\n\n**Q8: Typos and clarifications.**\n\nThe symbol $P$ in Equation (1) is actually the noisy point cloud $P_a$ for the initial step. We will correct the symbol and other typographical mistakes in our revision."}, {"review_id": "17aNKAtwyD", "reviewer": "Reviewer_hTqa", "summary": "The paper introduces  U-CAN , an unsupervised framework for point cloud denoising that leverages a  Consistency-Aware Noise2Noise Matching  approach. U-CAN employs a neural network to infer multi-step denoising paths for noisy point clouds, using a novel  Noise to Noise Matching loss  to learn denoising patterns without requiring clean ground truth data. Additionally, it introduces a  Denoising Consistency loss  to ensure geometric consistency across multiple noisy observations, enhancing robustness. The framework is evaluated on synthetic (PUNet) and real-world (Paris-rue-Madame) datasets, achieving state-of-the-art performance in unsupervised point cloud denoising and comparable results to supervised methods. U-CAN also demonstrates applicability to 2D image denoising (McMaster18 dataset) and unsupervised point cloud upsampling, showcasing its versatility.", "questions": "See weakness.", "limitations": "The authors adequately address limitations. They note the qualitative nature of evaluations on real-world data (Paris-rue-Madame) due to the lack of ground truth  and acknowledge challenges in predicting high-fidelity local geometries compared to supervised methods. The paper appropriately marks societal impact questions as “NA” (not provided in the excerpt but assumed per NeurIPS guidelines), as the work is foundational and does not involve high-risk applications. The transparency about limitations is commendable, and no critical points appear to be missing.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n\n1. The paper introduces U-CAN, an unsupervised framework that leverages consistency-aware Noise2Noise matching to denoise point clouds without clean supervision. By using a neural network to infer multi-step denoising paths and a novel loss function for statistical reasoning on noisy observations, U-CAN overcomes the need for manually annotated clean point clouds, addressing a key challenge in prior supervised methods . The framework's design, which adapts Noise2Noise to 3D point clouds via Earth Mover's Distance (EMD), effectively handles the unordered nature of point sets.\n\n2. The proposed Denoising Consistency Constraint (L_DC) ensures geometric consistency across denoised predictions from different noisy inputs, mitigating ambiguity in unsupervised learning. This constraint not only improves local geometry preservation in point clouds but also generalizes to 2D image denoising, demonstrating its versatility . The combination of L_N2N (Noise to Noise Matching loss) and L_DC enables U-CAN to produce high-fidelity results while maintaining computational efficiency. \n\n3. U-CAN outperforms state-of-the-art unsupervised methods in point cloud denoising, upsampling, and image denoising. \n\nWeaknesses :\n\n1. Unverified Effectiveness with Alternative Backbone Networks\nThe study focuses on a specific denoising network architecture but does not explore how the proposed Consistency-Aware Noise2Noise losses (Lₙ₂ₙ and L_DC) perform when integrated with other backbone networks (e.g., PointNet++,  or transformer-based architectures). Verifying their generality across different network designs is crucial to confirm the framework’s adaptability and robustness.\n\n2.Lack of Evaluation on Indoor Point Cloud Datasets\nThe paper does not assess U-CAN on indoor point cloud benchmarks such as ScanNet, which are critical for real-world applications in robotics, AR/VR, and autonomous interior navigation. Indoor scenes often contain complex structures (e.g., furniture, partitions) and varying noise distributions (e.g., sensor reflections or occlusions), posing unique challenges for denoising.", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely appreciate Reviewer hTqa for the acknowledgment of our work and constructive feedback. We respond to each question below.\n\n**Q1: Alternative backbone networks.**\n\nWe thank reviewer hTqa for the insightful suggestion regarding the integration of the proposed framework with alternative backbone networks. Following this advice, we replaced the EdgeConv-based denoising network with PointNet++ and PointTransformer to evaluate the generality of U-CAN across different architectures. The results are reported in Table F below.\n\n***Table F: Effectiveness of U-CAN with different backbones.***\n\n| Dataset: PU               |          | 10K, 1%   |         | 10K, 2%   |         | 10K, 3%   |         |\n|---------------------------|----------|----------|---------|----------|---------|----------|---------|\n| Ablation                  |          | CD       | P2M     | CD       | P2M     | CD       | P2M     |\n| U-CAN (PointNet++)        |          | 3.427    | 1.803   | 4.393    | 2.424   | 5.047    | 2.969   |\n| U-CAN (PointTransformer)  |          | 2.547    | 1.204   | 3.277    | 1.639   | 3.684    | 1.892   |\n| **Ours**                  |          | **2.497**| **1.105**| **3.234**| **1.255**| **3.666**| **1.842** |\n\nAs demonstrated, the U-CAN framework consistently achieves robust denoising performance across different backbone networks. PointNet++ is a relatively older backbone that provides stable but suboptimal results, while PointTransformer, a more modern architecture, achieves performance comparable to our default denoising model. Notably, we directly integrate these backbones into U-CAN without the need for manual tuning of settings or hyperparameters specific to each architecture. These results highlight the strong generality, adaptability, and robustness of the proposed framework.\n\n**Q2: Evaluation on indoor point cloud datasets like ScanNet.**\n\nWe sincerely thank the reviewer hTqa for the valuable advice and fully recognize the importance of evaluating U-CAN under real-world indoor scene scans. To provide a more comprehensive evaluation of U-CAN's performance, we conducted an experiment on the ScanNet dataset, a real-world indoor dataset consisting of noisy point clouds obtained from scanning sensors. These point clouds contain complex structures (e.g., furniture, partitions) and exhibit varying noise distributions (e.g., sensor reflections and occlusions). We apply U-CAN to predict denoised point clouds from these scans and report the numerical metrics comparing the denoised predictions with the ground truth clean meshes provided in the ScanNet dataset. The results, along with comparisons to state-of-the-art unsupervised point denoising methods, are presented in Table B below, where U-CAN achieves the best performance.\n\n\n***Table B. Comparisions under indoor ScanNet dataset.***\n\n| Method        | CD | P2M |\n|---------------|----------|----------|\n| DMR-TTD   | 2.629    |   2.381  |\n| ScoreDenoise-TTD  | 2.474     | 2.524     |\n| **Ours**      | **1.798**     | **1.897**     |\n\nU-CAN achieves superior performance on both the indoor and outdoor scene point clouds scanned in the real world, demonstrating its remarkable capability in real-world downstream applications in robotics, autonomous driving, AR/VR, and autonomous interior navigation."}]

Author rebuttal:

Meta-review: The paper initially received mixed reviews. The major concerns were:

1) computational cost of EMD? [gzhj]
2) needs more description about the noise distributions [25Zo]
3) performance under real world noise? [25Zo]
4) does U-can have advantage in model complexity? [25Zo]
5) core ideas from Noise2Noise for 2D image denoising and multi-step denoising [25Zo, y6U3]
6) missing baseline comparison [y6U3]
7) Why does the proposed method perform worse in P2M under low-noise levels? [y6U3]
8) missing ablation study on backbone networks [hTqa]
9) missing evaluation on indoor scenes [hTqa]

The authors wrote a response to address these points. After the discussion, gzhj and hTqa were satisfied and kept their ratings. y6U3 was also satisfied and updated to border accept. However, y6U3 still had reservations that the underlying principle is from Noise2NoiseMapping for 2d images, but acknowledged the differences in learning scheme, framework, and novelty of enforcing cross-scan consistency. 25Zo maintained their original rating of borderline reject, but did not give any particular comments about how the rebuttal failed to address their concerns. The final ratings were 4534.

After reading the paper, reviews, rebuttal, and discussions, the AC thought that the paper was sufficiently novel as it adapts the Noise2NoiseMapping principle from 2d images to point clouds, and addresses unique challenges that arise from this. The experiment results are compelling. The AC thought that 25Zo's comments were addressed well enough. Overall, the AC agrees with the positive reviewers and recommends Accept. 

The authors should revise the paper according to the reviews, rebuttal, and discussion.
Decision: Accept (poster)