arxiv: 2603.26588 · v2 · submitted 2026-03-27 · 💻 cs.CV · cs.LG

Recognition: 2 theorem links

· Lean Theorem

From Synthetic Data to Real Restorations: Diffusion Model for Patient-specific Dental Crown Completion

D\'avid Pukanec , Tibor Kub\'ik , Michal \v{S}pan\v{e}l

Authors on Pith no claims yet

Pith reviewed 2026-05-14 23:20 UTC · model grok-4.3

classification 💻 cs.CV cs.LG

keywords diffusion models3D shape completiondental restorationsynthetic datatooth crownmedical imagingcomputer visionconditional generation

0 comments

The pith

A diffusion model trained solely on synthetic incomplete teeth completes real dental crowns with minimal occlusion interference.

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

ToothCraft is a diffusion model that generates complete tooth crowns conditioned on the local anatomical context from incomplete inputs. The authors train it using an augmentation pipeline that artificially damages complete dental arch scans from public datasets, creating diverse synthetic defects without needing real incomplete examples. This enables the model to achieve 81.8% intersection over union and 0.00034 Chamfer distance on held-out synthetic tests, and to produce usable restorations on actual patient scans. A sympathetic reader would care because it offers a path to automated, data-efficient crown design in dentistry, where collecting matched incomplete-complete pairs is difficult. If successful, it reduces reliance on manual sculpting or large clinical datasets for prosthetic work.

Core claim

The paper claims that a conditioned 3D diffusion model for tooth crown completion, trained only on synthetically generated incomplete teeth derived from complete arch data, can reconstruct crowns accurately on synthetic cases and generalize directly to real patient incomplete teeth, producing crowns with minimal intersection against the opposing dentition.

What carries the argument

The ToothCraft conditioned diffusion model, which takes local anatomical context from surrounding teeth and generates the missing crown geometry via a trained denoising process.

If this is right

Real-world incomplete teeth can be completed automatically without additional real training data.
Generated crowns exhibit minimal intersection with opposing teeth, reducing occlusal interference risks.
The synthetic augmentation approach allows robust performance across varied defect types.
Quantitative metrics of 81.8% IoU and 0.00034 CD support practical utility on synthetic benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar synthetic defect generation could extend to other 3D medical restoration tasks like bone or organ completion.
Clinical adoption would likely need further testing for biocompatibility and long-term fit beyond geometric metrics.
The method opens the possibility of patient-specific designs in real-time dental CAD systems.

Load-bearing premise

The artificial defects produced by damaging complete arches sufficiently mimic the distribution and types of defects found in real clinical incomplete teeth.

What would settle it

A direct test on a collection of real incomplete tooth scans where the model's output crowns show substantial volumetric overlap with opposing dentition or deviate significantly from dentist-approved restorations.

Figures

Figures reproduced from arXiv: 2603.26588 by D\'avid Pukanec, Michal \v{S}pan\v{e}l, Tibor Kub\'ik.

**Figure 1.** Figure 1: High-level overview of tooth completion process. A unified model is conditioned on the local context, with the optional antagonist [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

**Figure 2.** Figure 2: Detailed overview of completion architecture. For the additional antagonist, the Contextual branch is duplicated, and feature [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Augmentation pipeline. Internal representation is denoted above the visualised meshes. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Visual representations of meshes obtained through the Marching Cubes algorithm on test set. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Examples of teeth completed by our network. All results were achieved using a single cohesive model, with human-designed [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Failure cases produced by our model. The most common [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

read the original abstract

We present ToothCraft, a diffusion-based model for the contextual generation of tooth crowns, trained on artificially created incomplete teeth. Building upon recent advancements in conditioned diffusion models for 3D shapes, we developed a model capable of an automated tooth crown completion conditioned on local anatomical context. To address the lack of training data for this task, we designed an augmentation pipeline that generates incomplete tooth geometries from a publicly available dataset of complete dental arches (3DS, ODD). By synthesising a diverse set of training examples, our approach enables robust learning across a wide spectrum of tooth defects. Experimental results demonstrate the strong capability of our model to reconstruct complete tooth crowns, achieving an intersection over union (IoU) of 81.8% and a Chamfer Distance (CD) of 0.00034 on synthetically damaged testing restorations. Our experiments demonstrate that the model can be applied directly to real-world cases, effectively filling in incomplete teeth, while generated crowns show minimal intersection with the opposing dentition, thus reducing the risk of occlusal interference. Access to the code, model weights, and dataset information will be available at: https://github.com/ikarus1211/VISAPP_ToothCraft

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ToothCraft trains a conditioned diffusion model on synthetic dental defects to complete 3D crowns, with decent synthetic metrics but only qualitative checks on real scans.

read the letter

The paper's core contribution is a diffusion model called ToothCraft that completes missing tooth crowns in 3D scans, conditioned on surrounding anatomy. They train it entirely on incomplete shapes created by an augmentation pipeline applied to public complete-arch datasets, then report 81.8% IoU and 0.00034 Chamfer distance on held-out synthetic tests. They also show a few real-scan examples where the outputs avoid obvious clashes with opposing teeth. The synthetic pipeline is the practical part here: it generates a range of defect types without needing real incomplete training data, which is a reasonable workaround for data scarcity in this domain. Releasing code, weights, and dataset details is also useful for follow-up work. The main limitation is the real-world claim. All quantitative numbers stay inside the synthetic test split that uses the same damage process as training, so we have no measured performance on actual clinical incompletenesses like caries, fractures, or preparation margins. The real cases are described qualitatively only, with no expert ground-truth comparisons or baseline methods. That leaves the generalization step untested in a measurable way. This work is aimed at researchers doing 3D generative modeling for medical or dental applications, especially those already using diffusion on point clouds or meshes. A reader looking for concrete conditioning tricks or synthetic-data recipes could pick up usable details. I would send it to peer review. The method is clearly described, the synthetic results are reproducible on the stated setup, and the data-release plan strengthens it, even though reviewers will likely press for quantitative real-patient validation and comparisons.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces ToothCraft, a conditioned diffusion model for completing dental crowns from incomplete tooth geometries. Trained exclusively on synthetically augmented incomplete teeth derived from complete dental arch datasets (3DS and ODD), it reports an IoU of 81.8% and Chamfer Distance of 0.00034 on a synthetic test set. The central claim is that the model can be applied directly to real-world patient cases, producing crowns with minimal intersection against opposing dentition.

Significance. If the synthetic-to-real generalization holds under quantitative scrutiny, the work could advance automated, patient-specific dental restoration by reducing reliance on scarce real incomplete training data. The explicit release of code, model weights, and dataset information is a clear strength for reproducibility.

major comments (3)

[Results] Results section: All quantitative metrics (IoU 81.8%, CD 0.00034) are confined to the synthetic test split generated by the same augmentation pipeline used for training. No quantitative evaluation (e.g., IoU, CD, or expert-rated occlusion scores) is provided on real incomplete patient scans with ground-truth completions, leaving the headline claim of direct real-world applicability only qualitatively supported.
[Methods] Methods, augmentation pipeline subsection: The claim that synthetically generated defects are representative of real clinical incompletenesses (caries, fractures, preparation margins) is not backed by any comparative distribution analysis or expert validation against clinical cases. This assumption is load-bearing for the generalization argument but remains untested.
[Experiments] Experiments: No non-diffusion baselines (e.g., traditional CAD completion or other generative models) are reported, so the relative benefit of the diffusion approach over simpler alternatives cannot be assessed from the given numbers.

minor comments (2)

[Abstract] Abstract and Results: Report standard deviations or confidence intervals alongside the single IoU and CD values to indicate variability across test cases.
[Figures] Figure 5 (qualitative real cases): Add explicit scale bars and clarify the units of the displayed meshes to allow readers to judge clinical relevance of the intersections shown.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive feedback. We address each major comment below and have revised the manuscript to improve clarity on evaluation limitations and add comparisons where possible.

read point-by-point responses

Referee: [Results] Results section: All quantitative metrics (IoU 81.8%, CD 0.00034) are confined to the synthetic test split generated by the same augmentation pipeline used for training. No quantitative evaluation (e.g., IoU, CD, or expert-rated occlusion scores) is provided on real incomplete patient scans with ground-truth completions, leaving the headline claim of direct real-world applicability only qualitatively supported.

Authors: We agree that quantitative metrics on real incomplete scans would strengthen the claims. However, real patient cases lack paired ground-truth complete crowns, precluding direct IoU or CD computation. We have expanded the results section with additional qualitative real-world examples, including multi-view visualizations of generated crowns and opposing dentition to demonstrate minimal interference. A new limitations subsection discusses the challenges of real-data evaluation and the role of synthetic training. This provides a more balanced presentation without overstating generalizability. revision: partial
Referee: [Methods] Methods, augmentation pipeline subsection: The claim that synthetically generated defects are representative of real clinical incompletenesses (caries, fractures, preparation margins) is not backed by any comparative distribution analysis or expert validation against clinical cases. This assumption is load-bearing for the generalization argument but remains untested.

Authors: The augmentation parameters were selected based on standard clinical descriptions of caries, fractures, and preparation margins from dental literature. We will add a supplementary figure and brief analysis comparing key geometric statistics (defect volume, surface area, and curvature distributions) between synthetic defects and a small set of anonymized real clinical examples. This provides supporting evidence for representativeness while noting that full expert validation was outside the current scope. revision: yes
Referee: [Experiments] Experiments: No non-diffusion baselines (e.g., traditional CAD completion or other generative models) are reported, so the relative benefit of the diffusion approach over simpler alternatives cannot be assessed from the given numbers.

Authors: We agree that baseline comparisons are important. In the revised manuscript we include two non-diffusion baselines: template-based nearest-neighbor completion and a 3D VAE completion model. On the synthetic test set the diffusion model achieves higher IoU and lower Chamfer distance than both, highlighting its advantage in modeling complex tooth morphology. We also briefly discuss why diffusion is suitable for handling high uncertainty in crown completion. revision: yes

standing simulated objections not resolved

Quantitative evaluation (IoU, CD, or expert scores) on real incomplete patient scans with ground-truth completions, as no such paired real data exists

Circularity Check

0 steps flagged

No circularity: training and evaluation remain independent of target claims

full rationale

The paper trains a conditioned diffusion model on incomplete tooth geometries produced by an augmentation pipeline applied to external public datasets (3DS, ODD). Quantitative metrics (IoU 81.8 %, CD 0.00034) are computed exclusively on a synthetically damaged held-out test split generated by the same pipeline. The claim of direct applicability to real-world cases rests on qualitative visual inspection and occlusion checks rather than any equation or fitted parameter that reduces to the input distribution by construction. No self-citations, uniqueness theorems, or ansatzes are invoked to justify core steps, and no derivation chain equates a prediction to its own training inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities beyond standard diffusion-model assumptions and the claim that the synthetic augmentation pipeline is sufficient; therefore the ledger is empty.

pith-pipeline@v0.9.0 · 5531 in / 1029 out tokens · 33311 ms · 2026-05-14T23:20:44.699385+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We present ToothCraft, a diffusion-based model for the contextual generation of tooth crowns, trained on artificially created incomplete teeth... achieving an intersection over union (IoU) of 81.8% and a Chamfer Distance (CD) of 0.00034 on synthetically damaged testing restorations.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The input of ToothCraft consists of the local anatomical context of the tooth to be completed... represented by a Signed Distance Field (SDF).

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages · 2 internal anchors

[1]

Teeth3ds: a benchmark for teeth segmentation and labeling from intra-oral 3d scans.arXiv e-prints, pages arXiv–2210, 2022

Achraf Ben-Hamadou, Oussama Smaoui, Houda Chaabouni-Chouayakh, Ahmed Rekik, Sergi Pujades, Edmond Boyer, Julien Strippoli, Aur ´elien Thollot, Hugo Setbon, Cyril Trosset, et al. Teeth3ds: a benchmark for teeth segmentation and labeling from intra-oral 3d scans.arXiv e-prints, pages arXiv–2210, 2022. 2, 3, 4

work page 2022
[2]

Exploring the use of gener- ative adversarial networks for automated dental preparation design

Imane Chafi, Ying Zhang, Yoan Ladini, Farida Cheriet, Julia Keren, and Franc ¸ois Guibault. Exploring the use of gener- ative adversarial networks for automated dental preparation design. InInternational Symposium on Biomedical Imaging (ISBI), 2025. 2

work page 2025
[3]

Diffcomplete: Diffusion-based generative 3d shape completion.Advances in neural information processing systems, 36:75951–75966,

Ruihang Chu, Enze Xie, Shentong Mo, Zhenguo Li, Matthias Nießner, Chi-Wing Fu, and Jiaya Jia. Diffcomplete: Diffusion-based generative 3d shape completion.Advances in neural information processing systems, 36:75951–75966,

work page
[4]

Shape completion using 3d-encoder-predictor cnns and shape synthesis

Angela Dai, Charles Ruizhongtai Qi, and Matthias Nießner. Shape completion using 3d-encoder-predictor cnns and shape synthesis. InProceedings of the IEEE conference on computer vision and pattern recognition, pages 5868–5877,

work page
[5]

Towards better healthcare: What could and should be automated?Techno- logical Forecasting and Social Change, 172:120967, 2021

Wolfgang Fruehwirt and Paul Duckworth. Towards better healthcare: What could and should be automated?Techno- logical Forecasting and Social Change, 172:120967, 2021. 2

work page 2021
[6]

Classifier-Free Diffusion Guidance

Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance.arXiv preprint arXiv:2207.12598, 2022. 2, 3

work page internal anchor Pith review Pith/arXiv arXiv 2022
[7]

Denoising diffu- sion probabilistic models.Advances in Neural Information Processing Systems (NeurIPS), 2020

Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffu- sion probabilistic models.Advances in Neural Information Processing Systems (NeurIPS), 2020. 2

work page 2020
[8]

Personalized dental crown design: A point-to-mesh completion network.Medi- cal Image Analysis (MedIA), 2025

Golriz Hosseinimanesh, Ammar Alsheghri, Julia Keren, Farida Cheriet, and Francois Guibault. Personalized dental crown design: A point-to-mesh completion network.Medi- cal Image Analysis (MedIA), 2025. 2, 3

work page 2025
[9]

3d dynamic prediction of missing teeth in diverse patterns via centroid-prompted diffusion model

Zongrui Ji, Na Li, Peng Xue, Yi Dong, and Lei Ma. 3d dynamic prediction of missing teeth in diverse patterns via centroid-prompted diffusion model. InInternational Confer- ence on Medical Image Computing and Computer-Assisted Intervention, pages 3–12. Springer, 2025. 2

work page 2025
[10]

Toothforge: Automatic dental shape generation using synchronized spectral embeddings

Tibor Kub ´ık, Franc ¸ois Guibault, MichalˇSpanˇel, and Herv ´e Lombaert. Toothforge: Automatic dental shape generation using synchronized spectral embeddings. InInternational Conference on Information Processing in Medical Imaging, pages 313–326. Springer, 2025. 2

work page 2025
[11]

Repaint: Inpainting using denoising diffusion probabilistic models

Andreas Lugmayr, Martin Danelljan, Andres Romero, Fisher Yu, Radu Timofte, and Luc Van Gool. Repaint: Inpainting using denoising diffusion probabilistic models. InProceed- ings of the IEEE/CVF conference on computer vision and pattern recognition, pages 11461–11471, 2022. 4

work page 2022
[12]

Diffusion probabilistic models for 3d point cloud generation

Shitong Luo and Wei Hu. Diffusion probabilistic models for 3d point cloud generation. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 2837–2845, 2021. 2

work page 2021
[13]

Autosdf: Shape priors for 3d comple- tion, reconstruction and generation

Paritosh Mittal, Yen-Chi Cheng, Maneesh Singh, and Shub- ham Tulsiani. Autosdf: Shape priors for 3d comple- tion, reconstruction and generation. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 306–315, 2022. 2

work page 2022
[14]

Sven M ¨uhlemann, Jenni Hjerppe, Christoph HF H ¨ammerle, and Daniel S Thoma. Production time, effectiveness and costs of additive and subtractive computer-aided manufactur- ing (cam) of implant prostheses: A systematic review.Clin- ical Oral Implants Research, 32:289–302, 2021. 1

work page 2021
[15]

Improved denoising diffusion probabilistic models

Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. InInternational conference on machine learning, pages 8162–8171. PMLR,

work page
[16]

Transfer learning for diffusion models

Yidong Ouyang, Liyan Xie, Hongyuan Zha, and Guang Cheng. Transfer learning for diffusion models. InAdvances in Neural Information Processing Systems, pages 136962– 136989. Curran Associates, Inc., 2024. 2

work page 2024
[17]

SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis

Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhorn, Jonas M ¨uller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion mod- els for high-resolution image synthesis.arXiv preprint arXiv:2307.01952, 2023. 2

work page internal anchor Pith review Pith/arXiv arXiv 2023
[18]

High-resolution image synthesis with latent diffusion models

Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bj ¨orn Ommer. High-resolution image synthesis with latent diffusion models. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684–10695, 2022. 2, 3

work page 2022
[19]

Attention is all you need.Advances in neural information processing systems, 30, 2017

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko- reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30, 2017. 2

work page 2017
[20]

Dual octree graph networks for learning adaptive volumetric shape rep- resentations.ACM Transactions on Graphics (TOG), 41(4): 1–15, 2022

Peng-Shuai Wang, Yang Liu, and Xin Tong. Dual octree graph networks for learning adaptive volumetric shape rep- resentations.ACM Transactions on Graphics (TOG), 41(4): 1–15, 2022. 4

work page 2022
[21]

A 3d dental model dataset with pre/post- orthodontic treatment for automatic tooth alignment.Scien- tific Data, 11(1):1277, 2024

Shaofeng Wang, Changsong Lei, Yaqian Liang, Jun Sun, Xianju Xie, Yajie Wang, Feifei Zuo, Yuxin Bai, Song Li, and Yong-Jin Liu. A 3d dental model dataset with pre/post- orthodontic treatment for automatic tooth alignment.Scien- tific Data, 11(1):1277, 2024. 2, 3, 4

work page 2024
[22]

Multimodal shape completion via conditional generative ad- versarial networks

Rundi Wu, Xuelin Chen, Yixin Zhuang, and Baoquan Chen. Multimodal shape completion via conditional generative ad- versarial networks. InEuropean Conference on Computer Vision (ECCV), 2020. 2

work page 2020
[23]

Snowflakenet: Point cloud completion by snowflake point deconvolution with skip-transformer

Peng Xiang, Xin Wen, Yu-Shen Liu, Yan-Pei Cao, Pengfei Wan, Wen Zheng, and Zhizhong Han. Snowflakenet: Point cloud completion by snowflake point deconvolution with skip-transformer. InProceedings of the IEEE/CVF Interna- tional Conference on Computer Vision (ICCV), pages 5499– 5509, 2021. 2

work page 2021
[24]

Grnet: Gridding resid- ual network for dense point cloud completion

Haozhe Xie, Hongxun Yao, Shangchen Zhou, Jiageng Mao, Shengping Zhang, and Wenxiu Sun. Grnet: Gridding resid- ual network for dense point cloud completion. InEuropean conference on computer vision, pages 365–381. Springer,

work page
[25]

Shapeformer: Transformer-based shape completion via sparse representa- tion

Xingguang Yan, Liqiang Lin, Niloy J Mitra, Dani Lischin- ski, Daniel Cohen-Or, and Hui Huang. Shapeformer: Transformer-based shape completion via sparse representa- tion. InIEEE/CVF Conference on Computer Vision and Pat- tern Recognition (CVPR), 2022. 2

work page 2022
[26]

Dcrownformer: Morphology-aware point- to-mesh generation transformer for dental crown prosthesis from 3d scan data of antagonist and preparation teeth

Su Yang, Jiyong Han, Sang-Heon Lim, Ji-Yong Yoo, Su- Jeong Kim, Dahyun Song, Sunjung Kim, Jun-Min Kim, and Won-Jin Yi. Dcrownformer: Morphology-aware point- to-mesh generation transformer for dental crown prosthesis from 3d scan data of antagonist and preparation teeth. In International Conference on Medical Image Computing and Computer-Assisted Intervent...

work page
[27]

Mvdc: A multi-view dental completion model based on contrastive learning

Xunyu Yang, Qingxin Deng, Minghan Huang, Landu Jiang, and Dian Zhang. Mvdc: A multi-view dental completion model based on contrastive learning. InICASSP 2025-2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pages 1–5. IEEE, 2025. 2

work page 2025
[28]

Pcn: Point completion network

Wentao Yuan, Tejas Khot, David Held, Christoph Mertz, and Martial Hebert. Pcn: Point completion network. In2018 in- ternational conference on 3D vision (3DV), pages 728–737. IEEE, 2018. 2

work page 2018
[29]

Adding conditional control to text-to-image diffusion models

Lvmin Zhang, Anyi Rao, and Maneesh Agrawala. Adding conditional control to text-to-image diffusion models. In Proceedings of the IEEE/CVF international conference on computer vision, pages 3836–3847, 2023. 2, 3

work page 2023