{"id":"451db0d7-d6a9-44fd-8eb4-429e8bf7895c","arxiv_id":"2507.13595","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Noisy SDF targets generated from a second, independently noisy point cloud can supervise a neural network to predict nearly clean signed distance fields.","lead":"This paper trains a 3D shape reconstruction network to produce clean signed-distance fields from noisy point clouds by comparing two noisy scans of the same object instead of using clean ground truth. A smart generalist might care because it shows a classic image-denoising trick can be transplanted to 3D, potentially reducing the need for expensive clean 3D labels.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central Noise2Noise claim depends on target unbiasedness, but Appendix A.4 proves it only for an idealized normal projection of a directly perturbed closest point; the actual frozen Point2SDF target is a learned regression on full noisy clouds, and its unbiasedness is neither proven nor directly…","rationale":"The reader's weakest assumption is exactly that the learned Point2SDF target is unbiased. I agree that this is the load-bearing premise, but my concern is slightly more specific: even the idealized target used in Appendix A.4 is not the one generated by the pipeline, because the selected closest point in a noisy cloud is an extremum over many perturbations, not a directly perturbed fixed point. This strengthens the case that the proof does not connect to the method. The paper's own experiments provide indirect evidence of bias sensitivity (nonzero-mean noise and LiDAR-style noise degrade the gains), but no direct bias measurement. Therefore the central claim is plausible and often confirmed empirically, but it remains conditional on a condition that has not been checked. A simple bias audit plus the bias-subtraction retraining would settle it. Since the reader already issued CONDITIONAL, my read does not move the verdict; it refines the reason. I do not see grounds for REJECT because the empirical results, especially the near-match of noisy and clean supervision in Table 7, strongly suggest the bias is small in the tested zero-mean settings; the missing piece is direct verification.","tokens_in":20197,"tokens_out":7385,"duration_ms":92324,"concrete_test":"Directly measure the bias of the frozen Point2SDF target on held-out ShapeNet meshes with the paper's noise settings. For sigma in {0.01, 0.02}, sample many independent noisy point clouds p2 per shape, draw query points q as in Section 4.2, and compute delta(q) = s2(q|p2) - s_clean(q) using the frozen 3DS2V target. Report E[delta | q] binned by signed distance to the surface and compare its magnitude to the point-noise standard deviation. If |E[delta]| is negligible relative to the noise level, the premise survives; if it is comparable or larger, Eq. (5) trains toward a biased target. A second decisive check is to subtract the measured bias from the targets and retrain the Table 7 Noisy(3DS2V) setup: if IoU/NC change materially, the learned \"denoising\" is partly bias reproduction rather than unbiased N2N estimation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (5) is a Noise2Noise objective only if E_{p2}[s2(q|p2)] equals the clean SDF value s(q); otherwise the global minimizer is E[s_clean(q)|p1] + E[b(q,p2)|p1], where b is target bias, so the model learns the bias instead of removing noise. The theoretical support in Section 4.1 (Analysis) and Appendix A.4 assumes the target is n^T(q - (p + eps)) with p the true closest point and eps zero-mean Gaussian. Nothing in the actual pipeline produces this target. The frozen 3DS2V sees a full noisy point cloud and was trained on clean-input/clean-SDF pairs, so for noisy inputs it is an extrapolation, not a conditional expectation; no unbiasedness is established for it. Moreover, even the idealized closest-point projection is not covered: the selected closest point is the minimizer over many independently perturbed points, an extremum statistic whose error is not zero-mean in general, so the first-order calculation in Appendix A.4 does not transfer to the real data-generation process. The nonzero-mean Gaussian experiments in Table 6 (e.g., F-Score decreases by 0.025 at mu=0.02) and the LiDAR-style experiments in Table A.12 are consistent with this failure mode: when the target carries bias, the denoising gain shrinks or reverses. Because the central claim that noisy supervision recovers the clean field rests entirely on target unbiasedness, and no direct bias measurement is reported, the claim is not fully established by the current evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20589,"tokens_out":8664,"duration_ms":89141,"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":[{"comment":"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.","section":"Section 4.1, Eq. (5); Appendix A.4"},{"comment":"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.","section":"Appendix A.4"},{"comment":"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":"Table 6; Table A.12"},{"comment":"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.","section":"Section 4.2 and Section 5.3"}],"minor_comments":[{"comment":"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":"Section 4.1, Eq. (5)"},{"comment":"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).","section":"Section 4.2, 'Point Sampling'"},{"comment":"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.","section":"Table 3 and Section 5.5"},{"comment":"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.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper has a useful empirical result: noisy SDF targets nearly match clean targets in a controlled comparison, and the method consistently improves over the strong 3DS2V baseline. The main issue is that the theoretical justification in Section 4.1 and Appendix A.4 does not apply to the actual pipeline, and the paper does not provide an alternative validation of the unbiasedness assumption. The authors should either strengthen the theory (e.g., for the learned target and the extremum selection) or reframe the claim as an empirical finding with a stated limitation. The reliance on a clean-pretrained target generator should be acknowledged in the abstract and main text to avoid overstating the 'noisy supervision only' contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat 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.\n\nThe 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.\n\nThat 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.\n\nThis 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.","headline":"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.","tokens_in":21090,"tokens_out":3830,"would_cite":true,"duration_ms":41272,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["neural signed distance fields","Noise2Noise denoising","point cloud surface reconstruction","noisy supervision","implicit neural representation","self-supervised 3D learning","3D shape reconstruction","deep learning"],"falsifier":"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.","tokens_in":19988,"feed_emoji":"🧊","tokens_out":13437,"duration_ms":128300,"temperature":0.7,"pith_summary":"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.","feed_headline":"Matching two noisy 3D fields learns the clean surface","feed_subtitle":"A Noise2Noise-style trick in signed-distance space matches clean-supervision accuracy without ground-truth shapes.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Establishes the Noise2Noise principle that minimizing MSE between two noisy observations converges to the clean signal, which the paper extends to 3D SDFs.","marker":"Lehtinen et al. (2018)"},{"why":"Supplies the 3DS2V architecture used as the denoising network, the frozen noisy-target generator, and the main baseline.","marker":"Zhang et al. (2023)"},{"why":"Prior Noise2Noise extension to point clouds using EMD-based soft correspondence; provides the noise-generation protocol and the comparison motivating coordinate-wise SDF matching.","marker":"Ma et al. (2023)"},{"why":"Supplies 3DILG as an alternative target generator and denoising backbone in the generalization ablation.","marker":"Zhang et al. (2022)"},{"why":"Provides the P2S method, the ABC/Famous/Real datasets, and the evaluation protocol used for out-of-distribution comparisons.","marker":"Erler et al. (2020)"},{"why":"PPSurf is a clean-supervised baseline trained on ABC that the paper compares against on noisy scans.","marker":"Erler et al. (2024)"},{"why":"Provides the ShapeNet benchmark used for the main noisy-versus-clean supervision experiments.","marker":"Chang et al. (2015)"},{"why":"Provides the ABC CAD dataset used for out-of-distribution training and evaluation.","marker":"Koch et al. (2019)"}],"fun_headline_variants":["Noise2Noise for 3D: clean SDFs from noisy pairs","Clean neural fields from two noisy point clouds","Denoising SDFs without ever seeing a clean one","Matching noisy signed distances reveals the true surface","Two noisy point sets learn a cleaner SDF"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Noise2Noise for 3D: clean SDFs from noisy pairs","Clean neural fields from two noisy point clouds","Denoising SDFs without ever seeing a clean one","Matching noisy signed distances reveals the true surface","Two noisy point sets learn a cleaner SDF"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000529,"raw_usage":{"total_tokens":2545,"prompt_tokens":938,"completion_tokens":1607,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":554,"completion_tokens_details":{"reasoning_tokens":1526}},"tokens_in":554,"tokens_out":1607,"duration_ms":12363,"temperature":1.0,"reasoning_tokens":1526,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:21:49.355192+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"3DILG: Irregular Latent Grids for 3D Generative Modeling","cited_arxiv_id":null,"evidence_quote":"Supplies 3DILG as an alternative target generator and denoising backbone in the generalization ablation."},{"cited_title":"J., and Wimmer, M","cited_arxiv_id":null,"evidence_quote":"Provides the P2S method, the ABC/Famous/Real datasets, and the evaluation protocol used for out-of-distribution comparisons."}],"review_version":1}