# LaGeM: A Large Geometry Model for 3D Representation Learning and Diffusion

arXiv: https://arxiv.org/abs/2410.01295 · HTML: https://mlsanity.com/paper/2410.01295/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 56 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 30 of 51)

- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [DreamGaussian: Generative Gaussian Splatting for Efficient 3D Content Creation](https://mlsanity.com/paper/2309.16653/) (2023)
- [Wonder3D: Single Image to 3D using Cross-Domain Diffusion](https://mlsanity.com/paper/2310.15008/) (2023)
- [Fantasia3D: Disentangling Geometry and Appearance for High-quality Text-to-3D Content Creation](https://mlsanity.com/paper/2303.13873/) (2023)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Google Scanned Objects: A High-Quality Dataset of 3D Scanned Household Items](https://mlsanity.com/paper/2204.11918/) (2022)
- [Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation](https://mlsanity.com/paper/2212.00774/) (2022)
- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [Magic123: One Image to High-Quality 3D Object Generation Using Both 2D and 3D Diffusion Priors](https://mlsanity.com/paper/2306.17843/) (2023)
- [Instant3D: Fast Text-to-3D with Sparse-View Generation and Large Reconstruction Model](https://mlsanity.com/paper/2311.06214/) (2023)
- [ABO: Dataset and Benchmarks for Real-World 3D Object Understanding](https://mlsanity.com/paper/2110.06199/) (2021)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [3D Neural Field Generation using Triplane Diffusion](https://mlsanity.com/paper/2211.16677/) (2022)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [ImageDream: Image-Prompt Multi-view Diffusion for 3D Generation](https://mlsanity.com/paper/2312.02201/) (2023)
- [Michelangelo: Conditional 3D Shape Generation based on Shape-Image-Text Aligned Latent Representation](https://mlsanity.com/paper/2306.17115/) (2023)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)

## Built on by (most cited first, 16 of 16)

- [Dora: Sampling and Benchmarking for 3D Shape Variational Auto-Encoders](https://mlsanity.com/paper/2412.17808/) (2024)
- [Sat2City: 3D City Generation from A Single Satellite Image with Cascaded Latent Diffusion](https://mlsanity.com/paper/2507.04403/) (2025)
- [iFlame: Interleaving Full and Linear Attention for Efficient Mesh Generation](https://mlsanity.com/paper/2503.16653/) (2025)
- [Hyper3D: Efficient 3D Representation via Hybrid Triplane and Octree Feature for Enhanced 3D Shape Variational Auto-Encoders](https://mlsanity.com/paper/2503.10403/) (2025)
- [Representing 3D Shapes With 64 Latent Vectors for 3D Diffusion Models](https://mlsanity.com/paper/2503.08737/) (2025)
- [DiMeR: Disentangled Mesh Reconstruction Model](https://mlsanity.com/paper/2504.17670/) (2025)
- [SOPHY: Learning to Generate Simulation-Ready Objects with Physical Materials](https://mlsanity.com/paper/2504.12684/) (2025)
- [Autoregressive Generation of Static and Growing Trees](https://mlsanity.com/paper/2502.04762/) (2025)
- [GarmentX: Autoregressive Parametric Representations for High-Fidelity 3D Garment Generation](https://mlsanity.com/paper/2504.20409/) (2025)
- [Sat2City v2: Native 3D City Asset Generation from a Single Satellite Image](https://mlsanity.com/paper/2606.24138/) (2026)
- [TopoMesh: High-Fidelity Mesh Autoencoding via Topological Unification](https://mlsanity.com/paper/2603.24278/) (2026)
- [Memorization in 3D Shape Generation: An Empirical Study](https://mlsanity.com/paper/2512.23628/) (2025)
- [High-Fidelity Medical Shape Generation via Skeletal Latent Diffusion](https://mlsanity.com/paper/2603.07504/) (2026)
- [ZipTok3D: High-Fidelity 3D Tokenization with Compact Token Prefixes](https://mlsanity.com/paper/2609.01740/) (2026)
- [NoiseSDF2NoiseSDF: Learning Clean Neural Fields from Noisy Supervision](https://mlsanity.com/paper/2507.13595/) (2025)
- [Generative Shape Reconstruction with Geometry-Guided Langevin Dynamics](https://mlsanity.com/paper/2603.27016/) (2026)

## Abstract (arXiv)

This paper introduces a novel hierarchical autoencoder that maps 3D models into a highly compressed latent space. The hierarchical autoencoder is specifically designed to tackle the challenges arising from large-scale datasets and generative modeling using diffusion. Different from previous approaches that only work on a regular image or volume grid, our hierarchical autoencoder operates on unordered sets of vectors. Each level of the autoencoder controls different geometric levels of detail. We show that the model can be used to represent a wide range of 3D models while faithfully representing high-resolution geometry details. The training of the new architecture takes 0.70x time and 0.58x memory compared to the baseline. We also explore how the new representation can be used for generative modeling. Specifically, we propose a cascaded diffusion framework where each stage is conditioned on the previous stage. Our design extends existing cascaded designs for image and volume grids to vector sets.