# LION: Latent Point Diffusion Models for 3D Shape Generation

1 NVIDIA 2 University of Toronto 3 Vector Institute
NeurIPS 2022

## News

event [Oct 2022] Project page released!
event [Oct 2022] Paper released on arXiv!
event [Aug 2022] LION got accepted to Advances in Neural Information Processing Systems (NeurIPS)!

## Abstract

Denoising diffusion models (DDMs) have shown promising results in 3D point cloud synthesis. To advance 3D DDMs and make them useful for digital artists, we require (i) high generation quality, (ii) flexibility for manipulation and applications such as conditional synthesis and shape interpolation, and (iii) the ability to output smooth surfaces or meshes. To this end, we introduce the hierarchical Latent Point Diffusion Model (LION) for 3D shape generation. LION is set up as a variational autoencoder (VAE) with a hierarchical latent space that combines a global shape latent representation with a point-structured latent space. For generation, we train two hierarchical DDMs in these latent spaces. The hierarchical VAE approach boosts performance compared to DDMs that operate on point clouds directly, while the point-structured latents are still ideally suited for DDM-based modeling. Experimentally, LION achieves state-of-the-art generation performance on multiple ShapeNet benchmarks. Furthermore, our VAE framework allows us to easily use LION for different relevant tasks: LION excels at multimodal shape denoising and voxel-conditioned synthesis, and it can be adapted for text- and image-driven 3D generation. We also demonstrate shape autoencoding and latent shape interpolation, and we augment LION with modern surface reconstruction techniques to generate smooth 3D meshes. We hope that LION provides a powerful tool for artists working with 3D shapes due to its high-quality generation, flexibility, and surface reconstruction.

## Method

We introduce the Latent Point Diffusion Model (LION), a DDM for 3D shape generation. LION focuses on learning a 3D generative model directly from geometry data without image-based training. Similar to previous 3D DDMs in this setting, LION operates on point clouds. However, it is constructed as a VAE with DDMs in latent space. LION comprises a hierarchical latent space with a vector-valued global shape latent and another point-structured latent space. The latent representations are predicted with point cloud processing encoders, and two latent DDMs are trained in these latent spaces. Synthesis in LION proceeds by drawing novel latent samples from the hierarchical latent DDMs and decoding back to the original point cloud space. Importantly, we also demonstrate how to augment LION with modern surface reconstruction methods to synthesize smooth shapes as desired by artists. LION has multiple advantages:

Expressivity: By mapping point clouds into regularized latent spaces, the DDMs in latent space are effectively tasked with learning a smoothed distribution. This is easier than training on potentially complex point clouds directly, thereby improving expressivity. However, point clouds are, in principle, an ideal representation for DDMs. Because of that, we use latent points, this is, we keep a point cloud structure for our main latent representation. Augmenting the model with an additional global shape latent variable in a hierarchical manner further boosts expressivity.

Varying Output Types: Extending LION with Shape As Points (SAP) geometry reconstruction allows us to also output smooth meshes. Fine-tuning SAP on data generated by LION's autoencoder reduces synthesis noise and enables us to generate high-quality geometry. LION combines (latent) point cloud-based modeling, ideal for DDMs, with surface reconstruction, desired by artists.

Flexibility: Since LION is set up as a VAE, it can be easily adapted for different tasks without retraining the latent DDMs: We can efficiently fine-tune LION's encoders on voxelized or noisy inputs, which a user can provide for guidance. This enables multimodal voxel-guided synthesis and shape denoising. We also leverage LION's latent spaces for shape interpolation and autoencoding. Optionally training the DDMs conditioned on CLIP embeddings enables image- and text-driven 3D generation.

## Generation Results (13-Classes Models)

Below we show samples from a LION model that was trained on shapes from multiple ShapeNet catgories, without any class-conditioning. We did on purpose not use conditioning to explore LION's scalability to diverse and multimodal datasets in the unconditional setting.

### Generating Samples with Fixed Shape Latents

The hierarchical VAE architecture of LION is crucial for scalability and capturing diverse shape data. It allows the model to learn a multimodal distribution over different categories without the need for class-conditioning. We find that the shape latent variables capture global shape, while the latent points model details. We validate this by fixing the shape variable to different values and only sampling different latent points.

For each group of shapes, we fix the shape latent variables and sample different latent points to generate the different shapes. We use the model that was trained on 13 ShapeNet categories.

## Generation Results (55-Classes Models)

Below we show samples from a LION model that was trained on all 55 ShapeNet categories jointly without any class-conditioning. Again, we did on purpose not use conditioning to explore LION's scalability to diverse and multimodal datasets in the unconditional setting. Even in that extreme setting, LION still generates reasonable shapes, thereby validating that the model has successfully learnt a highly complex and multimodal shape data distribution.

## More Results and Applications

Our main goal was to introduce a high-performance 3D shape generative model. Here, we qualitatively demonstrate how LION can be used for a variety of interesting applications.

### Shape Interpolation

LION can interpolate shapes by traversing the latent space (interpolation is performed in the latent diffusion models' prior space, using the Probability Flow ODE for deterministic DDM-generation). The generated shapes are clean and semantically plausible along the entire interpolation path.

### Fast Sampling with DDIM

LION's sampling time can be reduced by using fast DDM sampler, such as the DDIM sampler. DDIM sampling with 25 steps can already generate high-quality shapes, which takes less than 1 second. This enables real-time and interactive applications.

### Multimodal Generation

LION can synthesize different variations of a given shape, enabling multimodal generation in a controlled manner. This is achieved through a diffuse-denoise procedure, where shapes are diffused for only a few steps in the latent DDMs and then denoised again.

### Voxel-Conditioned Synthesis

Given a coarse voxel grid, LION can generate different plausible detailed shapes. In practice, an artist using a 3D generative model may have a rough idea of the desired shape. For instance, they may be able to quickly construct a coarse voxelized shape, to which the generative model then adds realistic details. We achieve this by fine-tuning our encoder networks on voxelized shapes, and performing a few steps of diffuse-denoise in latent space to generate various plausible detailed shapes.

### Single View Reconstruction

We qualitatively demonstrate how LION can be extended to also allow for single view reconstruction (SVR) from RGB data, using the approach from CLIP-Forge. We render 2D images from the 3D ShapeNet shapes, extract the images' CLIP image embeddings, and train LION's latent diffusion models while conditioning on the shapes' CLIP image embeddings. At test time, we then take a single view 2D image, extract the CLIP image embedding, and generate corresponding 3D shapes, thereby effectively performing SVR. We show SVR results from real RGB data.

### Text-Guided Generation

Using CLIP's text encoder, our method additionally allows for text-guided generation.

### Per-sample Text-driven Texture Synthesis

We apply Text2Mesh on some generated meshes from LION to additionally synthesize textures in a text-driven manner, leveraging CLIP. The original input meshes are generated by LION. This is only possible because LION can output practically useful meshes with its SAP-based surface reconstruction component (even though the backbone generative modeling component is point cloud-based).

## Paper

LION: Latent Point Diffusion Models for 3D Shape Generation

Xiaohui Zeng, Arash Vahdat, Francis Williams, Zan Gojcic, Or Litany, Sanja Fidler, Karsten Kreis

Advances in Neural Information Processing Systems (NeurIPS), 2022

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## Citation

@inproceedings{zeng2022lion,
title={LION: Latent Point Diffusion Models for 3D Shape Generation},
author={Xiaohui Zeng and Arash Vahdat and Francis Williams and Zan Gojcic and Or Litany and Sanja Fidler and Karsten Kreis},
booktitle={Advances in Neural Information Processing Systems (NeurIPS)},
year={2022}
}