# Deep Spectral Models for Robust Dental Shape Generation

arXiv: https://arxiv.org/abs/2606.31293 · HTML: https://mlsanity.com/paper/2606.31293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 15 of 15)

- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [PointLLM: Empowering Large Language Models to Understand Point Clouds](https://mlsanity.com/paper/2308.16911/) (2023)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [Explainable Anatomical Shape Analysis through Deep Hierarchical Generative Models](https://mlsanity.com/paper/1907.00058/) (2019)
- [Can point cloud networks learn statistical shape models of anatomies?](https://mlsanity.com/paper/2305.05610/) (2023)
- [From Mesh Completion to AI Designed Crown](https://mlsanity.com/paper/2501.04914/) (2025)
- [Discriminative and Generative Models for Anatomical Shape Analysison Point Clouds with Deep Neural Networks](https://mlsanity.com/paper/2010.00820/) (2020)
- [ToothForge: Automatic Dental Shape Generation using Synchronized Spectral Embeddings](https://mlsanity.com/paper/2506.02702/) (2025)
- [Point-Based Shape Representation Generation with a Correspondence-Preserving Diffusion Model](https://mlsanity.com/paper/2508.03925/) (2025)

## Abstract (arXiv)

Accurate modeling of dental crown morphology is fundamental for diagnosis, orthodontic planning, and computer-aided restoration design. However, datasets suitable for training such models are typically limited in size. We present ToothForge, a deep spectral generative framework that models dental crown geometries from compact, intrinsic representations. By operating in the spectral domain, ToothForge learns a latent manifold of 3D tooth shapes through synchronized spectral embeddings, ensuring consistent modeling across samples with varying connectivity. Spectral synchronization mitigates the instability of Laplace-Beltrami eigenbases and enables efficient learning in a low-dimensional space. The framework is thoroughly evaluated through robustness analysis, ablation studies, and benchmarking against PCA-based statistical shape models and point-based generative frameworks. Results show that synchronized spectral modeling achieves reconstruction and generative performance comparable to or exceeding spatial approaches, while maintaining compactness and geometric interpretability. Together, the compact synchronized coefficients and low-dimensional learning space make the framework particularly suitable for limited datasets, as often encountered in dental and medical domains, and applicable in real-world scenarios where guaranteeing consistent connectivity across shapes from various clinics is unrealistic.