# Learning to Tessellate: Point Cloud Generation via Recursive Spectral Partitioning

arXiv: https://arxiv.org/abs/2608.02432 · HTML: https://mlsanity.com/paper/2608.02432/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Builds on (most cited first, 30 of 33)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Autoregressive Image Generation using Residual Quantization](https://mlsanity.com/paper/2203.01941/) (2022)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [RoboGen: Towards Unleashing Infinite Data for Automated Robot Learning via Generative Simulation](https://mlsanity.com/paper/2311.01455/) (2023)
- [Open-MAGVIT2: An Open-Source Project Toward Democratizing Auto-regressive Visual Generation](https://mlsanity.com/paper/2409.04410/) (2024)
- [EmbodiedScan: A Holistic Multi-Modal 3D Perception Suite Towards Embodied AI](https://mlsanity.com/paper/2312.16170/) (2023)
- [PointGPT: Auto-regressively Generative Pre-training from Point Clouds](https://mlsanity.com/paper/2305.11487/) (2023)
- [FlexTok: Resampling Images into 1D Token Sequences of Flexible Length](https://mlsanity.com/paper/2502.13967/) (2025)
- [PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention](https://mlsanity.com/paper/1810.05591/) (2018)
- [EmbodiedOcc: Embodied 3D Occupancy Prediction for Vision-based Online Scene Understanding](https://mlsanity.com/paper/2412.04380/) (2024)
- [Scalable Image Tokenization with Index Backpropagation Quantization](https://mlsanity.com/paper/2412.02692/) (2024)
- [Autoregressive 3D Shape Generation via Canonical Mapping](https://mlsanity.com/paper/2204.01955/) (2022)
- [Frequency Autoregressive Image Generation with Continuous Tokens](https://mlsanity.com/paper/2503.05305/) (2025)
- [G3PT: Unleash the power of Autoregressive Modeling in 3D Generation via Cross-scale Querying Transformer](https://mlsanity.com/paper/2409.06322/) (2024)
- [RecDreamer: Consistent Text-to-3D Generation via Uniform Score Distillation](https://mlsanity.com/paper/2502.12640/) (2025)
- [D-AR: Diffusion via Autoregressive Models](https://mlsanity.com/paper/2505.23660/) (2025)
- [PointNSP: Autoregressive 3D Point Cloud Generation with Next-Scale Level-of-Detail Prediction](https://mlsanity.com/paper/2510.05613/) (2025)
- [PDT: Point Distribution Transformation with Diffusion Models](https://mlsanity.com/paper/2507.18939/) (2025)

## Abstract (arXiv)

Autoregressive models have emerged as an effective paradigm for point cloud generation. However, most existing approaches rely on heuristic tokenization strategies, such as spatial sorting or stochastic downsampling, which often disrupt intrinsic point cloud topology and weaken the structural coherence of the generated shapes. In this paper, we present PointRSP, an autoregressive framework that reformulates point cloud generation as a topology-preserving tessellation process via recursive spectral partitioning. Instead of constructing token sequences heuristically, we introduce a topology-aware partitioning autoencoder that decomposes an unstructured point cloud into a non-balanced binary tree through a hybrid recursive spectral partitioning strategy. This hierarchical representation provides a deterministic geometric blueprint that preserves topological relationships while capturing multiscale structural dependencies within a quantized latent space. To synthesize shapes in this space, we propose a dual-stream cascaded generator that jointly models structural evolution and feature synthesis. In addition, we design a geometry-calibrated positional encoding mechanism that anchors latent embeddings using multi-scale structural centers, which stabilizes cascaded generation during the early stages of structural formation. Extensive experiments show that PointRSP achieves state-of-the-art performance in generation quality and diversity, demonstrating strong generalization across complex 3D topologies.