NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision

Nick Barnes; Ruikai Cui; Shi Qiu; Tengkai Wang; Weihao Li

REVIEW 4 major objections 4 minor 15 references

NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper establishes that a clean neural signed distance field can be learned from noisy point clouds alone by minimizing squared error between two noisy SDF fields at identical query coordinates, nearly matching clean-supervision…

desk verdict A practical N2N-style SDF denoiser with solid experiments, but the unbiasedness proof only covers an idealized target, not the frozen teacher network the method actually uses. read the letter →

arxiv 2507.13595 v3 pith:KBFH3XQT submitted 2025-07-18 cs.CV

Tengkai Wang , Weihao Li , Ruikai Cui , Shi Qiu , Nick Barnes This is my paper · ORCID

classification cs.CV

keywords neuralsigneddistancefieldsNoise2Noisedenoisingpointcloudsurfacereconstructionnoisysupervisionimplicitrepresentationself-supervised3Dlearningshapedeep

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to show that the Noise2Noise trick, which cleaned up 2D images by training on pairs of noisy images alone, can be transplanted to 3D surface reconstruction. Its key move is to work not with raw point clouds, where points do not line up between two noisy scans, but with neural signed distance fields, where every query coordinate has a corresponding value in each noisy reconstruction. The network is trained to predict the SDF of one noisy point cloud while matching, with plain mean-squared error, the noisy SDF produced from a second noisy point cloud of the same shape. On ShapeNet this makes noisy supervision nearly as good as clean supervision, with IoU 0.927 versus 0.939 and normal consistency 0.966 versus 0.970 at the lower noise level. If this holds, clean 3D ground truth is not needed to train robust surface reconstruction from noisy scans.

What carries the argument

The machinery is a coordinate-wise correspondence in signed-distance space. A signed distance function maps every query point $q\in\mathbb{R}^3$ to its signed distance from the surface, so two separately generated noisy SDF fields of the same shape can be compared at identical coordinates $q$. The training loss $L(\theta)=\mathbb{E}[|\hat{s}(q|p_1)-s_2(q|p_2)|^2]$ is exactly the Noise2Noise mean-squared-error objective, with a frozen point-to-SDF network (3DS2V with fixed weights) supplying the noisy target $s_2$ and the trainable denoising network, a 3DS2V-style transformer with a frozen encoder and fine-tuned decoder, supplying the prediction $\hat{s}$. A first-order analysis shows that when the closest surface point is perturbed by zero-mean Gaussian noise, the noisy target is an unbiased estimate of the clean SDF to first order, which is what lets plain MSE denoise instead of averaging white noise.

What would settle it

Take a shape with a known ground-truth SDF, sample many point clouds with zero-mean Gaussian noise, run the frozen Point2SDF target network on each, and average the signed difference between target SDF and ground-truth SDF over a fixed grid of query points; a nonzero average near sharp edges or thin structures would show the target is biased, so the NoiseSDF2NoiseSDF fixed point is not the clean surface.

Watch

Extended reading notes

Core claim

The central claim is that a clean neural signed distance function can be learned from noisy supervision, without ever seeing a clean SDF, by exploiting coordinate-wise correspondence between two noisy fields. Given independent noisy point clouds $p_1$ and $p_2$ of the same shape, the denoising network predicts an SDF value at a query point $q$ from $p_1$, and the frozen Point2SDF network produces the noisy target SDF at the same $q$ from $p_2$. Minimizing the expected squared error between these values has the Noise2Noise property: because perturbing the closest surface point with zero-mean Gaussian noise makes the target's expectation equal the clean SDF to first order, the prediction is driven toward the clean surface. Empirically, noisy supervision nearly matches clean supervision (IoU 0.927 vs 0.939, NC 0.966 vs 0.970 on ShapeNet at $\sigma=0.01$) and beats the frozen 3DS2V baseline at both tested noise levels. The framework also transfers to ABC, Famous, and Real scans and remains effective when 3DS2V is replaced by 3DILG as target generator and denoising backbone.

Load-bearing premise

The load-bearing premise is that the frozen point-to-SDF network's noisy signed-distance targets are unbiased, meaning their expected value at every query point equals the true distance; the paper proves this only for an idealized normal-projection target, and a biased learned target would bias the reconstructed surface.

Editorial extensions

If this is right

Noisy supervision is nearly equivalent to clean supervision on ShapeNet at noise level 0.01, with IoU 0.927 versus 0.939 and normal consistency 0.966 versus 0.970, so clean ground truth may be unnecessary for training surface reconstruction networks.
The advantage over the 3DS2V baseline grows with noise: at noise level 0.02 the method gains +0.080 IoU and +0.135 normal consistency on average.
The model generalizes out of distribution: trained on ABC, it achieves competitive mean normal consistency on the Famous and Real scan datasets at noise level 0.01 (0.847), above clean-supervised data-driven baselines.
The framework is robust to component choice: replacing 3DS2V with 3DILG for both the noisy target and the denoising backbone still yields IoU 0.907 on the Chair subset at noise level 0.01.
Inference is a single forward pass, and optional test-time optimization improves Chamfer distance enough to beat the per-shape N2NM baseline at medium noise while remaining orders of magnitude faster.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Not tested in the paper: using a geometric, non-learned SDF estimator as the noisy target would match the idealized unbiased target in the proof more closely and could remove dependence on a pretrained Point2SDF network.
The same coordinate-wise correspondence logic should apply to other implicit field types, such as occupancy or unsigned distance fields, whenever two noisy observations can be evaluated at shared query coordinates; the fixed point will be clean only if the per-coordinate noise is zero-mean.
The small gap between noisy and clean supervision (IoU 0.927 vs 0.939) likely measures bias in the frozen target generator rather than irreducible observation noise, so calibrating or averaging multiple target generators could close most of that gap.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The main empirical result is real: training a 3DS2V-style SDF network against a frozen 3DS2V teacher that sees a second noisy point cloud gets you almost all the way to clean supervision (Table 7: 0.927 IoU vs 0.939). The experiments are thorough — ShapeNet, ABC, Famous, Real, several noise types, and an explicit comparison between noisy and clean targets. That makes the paper worth reading if you work on surface reconstruction from noisy scans.

What is genuinely new is the specific setup: a generalizable denoiser trained with coordinate-wise MSE against a frozen Point2SDF target, rather than per-shape overfitting. The inference is orders of magnitude faster than N2NM. The novelty claim is a bit overstated though: N2NM already applies noise-to-noise to SDFs, just with soft correspondences and per-shape optimization.

The soft spot is the theoretical story. The paper claims the loss in Eq. (5) works because the noisy SDF targets are unbiased estimates of the clean SDF. The proof in Appendix A.4 is for an idealized target: the normal projection of a perturbed closest point with zero-mean Gaussian noise. The actual target is the output of a pretrained 3DS2V network on a full noisy point cloud. Nobody has shown that output is unbiased. In fact, the closest point is a minimum over many perturbed points, so its error is not zero-mean in general. The biased-noise experiments (Table 6) are consistent with this: at mu=0.02 the F-Score drops by 0.025. The LiDAR-style experiments (Table A.12) also show shrinking gains. So the unbiasedness premise is not established for the real pipeline.

That said, the method works empirically, and the paper is honest enough to list dependence on the target generator as a limitation. The authors should either prove unbiasedness for the actual target or drop the unbiasedness story and frame this as a regularized training strategy. They should also measure target bias directly, and compare with N2NM on the same benchmark under the same protocol — the current comparison is only on Famous with test-time optimization.

This paper is for people doing 3D reconstruction from noisy point clouds. It deserves a serious referee; the experimental core is solid and the idea is useful even if the theory is overclaimed. I would engage with it, but push for revision that either fixes the theoretical claim or drops it.

Referee Report

4 major / 4 minor

Summary. The paper proposes NoiseSDF2NoiseSDF, a method for learning clean neural signed distance functions (SDFs) from noisy point clouds by extending the Noise2Noise (N2N) principle to 3D neural fields. The training pipeline uses two independently corrupted point clouds of the same shape: one is encoded by a denoising network (based on 3DS2V) to predict SDF values at query points, while the other is passed through a frozen Point2SDF network (also 3DS2V) to generate noisy SDF targets; the two sets of SDF values are compared at shared query coordinates with an MSE loss. The authors claim that coordinate-wise correspondence in SDF space makes the N2N concept applicable, enabling the network to denoise implicitly. Experiments on ShapeNet, ABC, Famous, and Real datasets show that the method outperforms the 3DS2V baseline under Gaussian noise at σ=0.01 and σ=0.02, and that noisy supervision nearly matches clean supervision (Table 7: IoU 0.927 vs 0.939, NC 0.966 vs 0.970). The paper also includes ablations on noise types, target generators, and denoising network components.

Significance. If the central claim holds, this is a meaningful extension of the Noise2Noise paradigm from 2D images to 3D neural fields, with practical relevance for reconstructing surfaces from noisy scanner data. The paper's strengths include a controlled experiment showing that noisy SDF targets achieve performance close to clean targets (Table 7), consistent improvements over the 3DS2V baseline across multiple ShapeNet categories (Tables 1 and 2), and evaluations on out-of-distribution datasets (ABC, Famous, Real) with comparisons against several strong baselines. The ablations on different target generators (3DILG vs 3DS2V) and on fine-tuning strategies (Table 8) provide useful information about the method's generality. However, the theoretical justification for why the N2N objective recovers the clean field is not established for the actual pipeline, and the paper's claims therefore outrun its current evidence.

major comments (4)

[Section 4.1, Eq. (5); Appendix A.4] The Noise2Noise argument for Eq. (5) requires that the noisy target be unbiased conditional on the query point, i.e., E_{p2}[s2(q|p2)] = s(q). Appendix A.4 proves this only for an idealized target of the form n^T(q - (p + ε)) with p the true closest point and ε zero-mean Gaussian. The actual target is the output of a frozen 3DS2V network trained on clean point-cloud/SDF pairs and evaluated on full noisy point clouds. For this learned regression, no unbiasedness argument is given; the network operates outside its training distribution on noisy inputs, and its errors may be systematically biased (e.g., smoothing of high-curvature features). Without a proof for the actual target generator or a direct measurement of E[s2(q|p2)] versus the clean SDF s(q), the loss in Eq. (5) may be minimizing squared error to a biased target, and the global minimizer becomes E[s(q)|p1] + E[b(q,p2)|p1] where b is the target bias. This is load-bearing because the paper's central claim that clean fields are recovered from noisy supervision rests entirely on target unbiasedness.
[Appendix A.4] Even for the idealized closest-point model, the first-order unbiasedness calculation does not transfer to the actual data-generation process. The noisy SDF target in the pipeline is not formed by perturbing a single known closest point; it is the output of a network that sees a point cloud in which the nearest neighbor to a query is the minimum over many (2048) independently perturbed surface points. The error of the nearest-neighbor point under additive zero-mean Gaussian noise is an extremum statistic: the minimum of many Gaussian variables has a non-zero (negative) mean, so E[ε] ≠ 0 and consequently E[δs] ≈ -n^T E[ε] ≠ 0. The analysis in Appendix A.4 treats ε as a single zero-mean perturbation and therefore does not apply. The authors should either analyze the extremum-statistics issue or explicitly weaken the theoretical claim to a heuristic motivation for the method.
[Table 6; Table A.12] The experimental results under biased noise are consistent with the failure mode predicted by the biased-target argument, but the paper does not discuss them in those terms. In Table 6, as the mean of the Gaussian noise increases from μ=0 to μ=0.02, the gains over the 3DS2V baseline shrink monotonically, and at μ=0.02 the F-Score drops below the baseline (0.524 vs 0.549). Under LiDAR-style structured noise in Table A.12, the relative improvements at the high corruption level are much smaller (CD 0.052 vs 0.059, F1 0.601 vs 0.518) than under zero-mean Gaussian noise. These observations indicate that the method is effective primarily when the noise is zero-mean and symmetric, which is exactly the condition under which the Noise2Noise unbiasedness assumption holds. The paper should acknowledge this limitation and connect it to the theoretical analysis, rather than reporting the results without interpretation.
[Section 4.2 and Section 5.3] The paper's use of a frozen Point2SDF target generator trained on clean data is a significant caveat to the 'no clean supervision' framing. Section 5.3 states that 'we do not use any paired noisy point clouds and clean SDFs throughout the entire training process,' and Section 5.2 says the model is trained 'without relying on any clean ground-truth' on the ABC/Famous/Real datasets. These statements are technically correct for the denoising network's training, but the target generator (3DS2V) itself was pretrained on clean point clouds and clean SDF labels. The method therefore still requires clean supervision on some training corpus, which weakens the motivation of learning when clean labels are impractical. The paper should state this explicitly and discuss how the approach relates to settings where no clean data is available at all.

minor comments (4)

[Section 4.1, Eq. (5)] The loss in Eq. (5) samples q uniformly from R^3, but the implementation described in Section 4.2 samples query points from a bounded cube (the normalized shape space) and additionally uses 50% near-surface query points derived from the noisy point clouds. The notation U(R^3) is misleading and should be changed to reflect the actual bounded sampling domain and the non-uniform mix of query point types.
[Section 4.2, 'Point Sampling'] The sentence 'To reduce dependency on the original clean surface, we directly use the two input noisy point clouds as the near-surface query points' is unclear: using noisy points as queries does not obviously reduce dependency on the clean surface, and the intended meaning should be stated more precisely (e.g., avoiding ground-truth mesh-based query sampling).
[Table 3 and Section 5.5] In Table 3, the 'mean (all)' row reports values with inconsistent decimal places across methods (e.g., P2S 0.761, Ours 0.819), and the F-Score for Ours at ABC(σ=0.02) is 0.724, which is well below several baselines; this result deserves a comment in the text. Additionally, Section 5.5 lists 'NC/Mesh NC/F-Score' as a sequence without indicating that Mesh NC is a separate metric where lower is better, which can confuse readers.
[General] The paper does not mention whether code or trained models will be released; providing this information would aid reproducibility and is customary for this type of submission.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is validated against external ground-truth metrics and clean-supervision baselines; the target-unbiasedness gap is a correctness concern, not a by-construction reduction.

full rationale

The paper's central derivation chain is not circular. Equation (5) defines a Noise2Noise-style MSE loss between the predicted SDF from one noisy point cloud and a target SDF generated by a frozen Point2SDF network from another noisy point cloud. The theoretical support in Section 4.1 and Appendix A.4 proves unbiasedness for an idealized target defined as a normal projection from a perturbed closest point (Eq. 8), but the implemented target is the output of a learned 3DS2V network (Section 4.2). This is a genuine gap between theory and implementation: the unbiasedness of the actual learned target is asserted rather than proven. However, this is an evidential or correctness limitation, not a circular reduction. The paper does not define the actual target to be the idealized projection, and it does not fit any parameter to the ground-truth SDF and then rename the fit as a prediction. The central empirical claim is independently checkable: results are reported against external ground-truth geometry via IoU, Chamfer Distance, F1, and Normal Consistency, and against a clean-supervision variant in Table 7 where noisy supervision nearly matches clean supervision. The comparison with the 3DS2V baseline is also not forced by construction, since Table 8 shows that randomly initializing the decoder or the entire network preserves performance, indicating the gains are not simply inherited pretrained weights. The self-citations present (e.g., Cui et al. 2024, Hong et al. 2022, Du et al. 2023) are background references for neural fields and weakly supervised learning and are not load-bearing for the main result. Thus, while the theoretical justification is incomplete, no step reduces by definition to its own inputs, and the paper's conclusions are externally falsifiable rather than circular.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method's claim to learn from noisy supervision rests on the assumption that noisy targets from a pretrained Point2SDF are unbiased and that clean-data pretraining is available. The central free parameters are standard training hyperparameters chosen without sensitivity analysis.

free parameters (4)

Gaussian noise standard deviations = 0.01 and 0.02
Chosen by hand following N2NM; defines the corruption regime and is not swept systematically.
near-surface query fraction = 0.5
Half of query points are taken from the noisy input point clouds and half are uniform; this choice is not ablated.
point cloud size = 2048
Sample size for both input and target point clouds; sparse by design and not swept.
query point count = 8192
Number of query points sampled online per training step; not swept.

assumptions (5)

standard math The signed distance function satisfies the Eikonal equation |nabla phi(x)| = 1 and the closest-point decomposition q = p + s n.
Used in Appendix A.4 to derive first-order unbiasedness of the noisy SDF target.
standard math Zero-mean Gaussian perturbation of the closest surface point produces a noisy SDF target that is unbiased to first order, E[tilde_s(q)] = s(q).
Derived in Appendix A.4 under a normal-projection noise model; this result is the theoretical basis for the MSE loss.
ad hoc to paper The frozen Point2SDF network's outputs on noisy point clouds are unbiased, independent noisy estimates of the clean SDF.
Assumed when using s2(q|p2) from a frozen learned network as the target in Eq. (5); never verified, and Appendix A.4 only proves this for an idealized normal-projection target, not for a learned network.
domain assumption Two independently corrupted point clouds of the same underlying shape are available during training.
Fundamental to the Noise2Noise setup; applies to synthetic Gaussian noise and the LiDAR-style model in Appendix A.3.3.
ad hoc to paper A clean-trained Point2SDF model is available, and the denoising network is initialized from that model's weights.
The method assumes access to a pretrained clean-data Point2SDF for target generation; without it there is no noisy target generator, so the 'no clean supervision' claim is conditional on an existing clean-data model.

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Cite this review

Pith. "Pith review of NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision." pith.science (2026). https://pith.science/paper/KBFH3XQT

@misc{pith2026250713595,
  author       = {Pith},
  title        = {Pith review of: NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBFH3XQT}},
  note         = {Machine review of arXiv:2507.13595}
}

read the original abstract

Reconstructing accurate implicit surface representations from point clouds remains a challenging task, particularly when data is captured using low-quality scanning devices. These point clouds often contain substantial noise, leading to inaccurate surface reconstructions. Inspired by the Noise2Noise paradigm for 2D images, we introduce NoiseSDF2NoiseSDF, a novel method designed to extend this concept to 3D neural fields. Our approach enables learning clean neural SDFs from noisy point clouds through noisy supervision by minimizing the MSE loss between noisy SDF representations, allowing the network to implicitly denoise and refine surface estimations. We evaluate the effectiveness of NoiseSDF2NoiseSDF on benchmarks, including the ShapeNet, ABC, Famous, and Real datasets. Experimental results demonstrate that our framework significantly improves surface reconstruction quality from noisy inputs.

Figures

Figures reproduced from arXiv: 2507.13595 by the authors.

**Figure 1.** Comparison of coordinate correspondences: (a) Pixel coordinates represent correspondences between two noisy images of the same scene. In contrast, (b) point coordinates do not exhibit correspondences between two noisy point clouds of the same shape. (c) SDF coordinates establish correspondences between two noisy neural fields representing the same shape. generated by off-the-shelf point-to-SDF methods, as the superv… view at source ↗

**Figure 2.** The training pipeline of the NoiseSDF2NoiseSDF framework. Given two independent noisy point clouds p1 and p2 of the same underlying shape, p1 is fed into the denoising network to predict a smoothed SDF sˆ, while p2 is passed through a Point2SDF network to generate a noisy SDF s2. Both SDFs are evaluated at a shared set of query points q, and their mean squared error is used to update the denoising network weights. S… view at source ↗

**Figure 3.** Comparison on the ShapeNet dataset. The first row shows Gaussian noise with σ = 0.01, and the second row with σ = 0.02. Ours produces smoother reconstructions, better aligning with the underlying surfaces compared to baseline [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Visualization of surface reconstruction under Gaussian noise (σ = 0.01 and 0.02), comparing two overfitting-based methods (PGR (Lin et al., 2022) and SAP-O (Peng et al., 2021)), three data-driven approaches (P2S (Erler et al., 2020), PPSurf (Erler et al., 2024), 3DS2V …

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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NumGrad-Pull: Numerical Gradient Guided Tri-plane Representation for Surface Reconstruction from Point Clouds

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PatchNets: Patch-based generaliz- able deep implicit 3D shape representations

Tretschk, E., Tewari, A., Golyanik, V ., Zollh¨ofer, M., Stoll, C., and Theobalt, C. PatchNets: Patch-based generaliz- able deep implicit 3D shape representations. InComputer Vision–ECCV 2020: 16th European Conference, Glas- gow, UK, August 23–28, 2020, Proceedings, Part XVI 16, pp. 293–309. Springer,

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The value of MNC is averaged over all edges, and typically falls in the range [0,2] , where lower values correspond to smoother and more consistent surface geometry

and (be −v 0)×(v 1 −v 0), and their cosine similarity measures the local smoothness across the edge. The value of MNC is averaged over all edges, and typically falls in the range [0,2] , where lower values correspond to smoother and more consistent surface geometry. Appendix A.2. More Visualization GT Noise-0.01 SDF2SDF PGR SAP-O P2S PPSurf 3DS2V Ours GT ...

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Approximating the signed distance with respect to the perturbed reference˜pand treatingnas constant to first order, we obtain ˜s≈n⊤(q−˜p) =n ⊤(q−(p+ε)) =n ⊤(q−p)−n ⊤ε≈s−n ⊤ε

Thus, near p the signed distance is approximately the projection onto the normal. Approximating the signed distance with respect to the perturbed reference˜pand treatingnas constant to first order, we obtain ˜s≈n⊤(q−˜p) =n ⊤(q−(p+ε)) =n ⊤(q−p)−n ⊤ε≈s−n ⊤ε. Hence, δs= ˜s−s≈ −n⊤ε, 15 NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision whi...

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