main result
Our method, the Quartet of Diffusions, harmoniously orchestrates an interpretable and controllable pipeline for structure-aware, high-quality, diverse, and efficient point cloud generation guided by part and symmetry clues.

Abstract

We introduce the Quartet of Diffusions, a structure-aware point cloud generation framework that explicitly models part composition and symmetry. Unlike prior methods that treat shape generation as a holistic process or only support part composition, our approach leverages four coordinated diffusion models to learn distributions of global shape latents, symmetries, semantic parts, and their spatial assembly. This structured pipeline ensures guaranteed symmetry, coherent part placement, and diverse, high-quality outputs. By disentangling the generative process into interpretable components, our method supports fine-grained control over shape attributes, enabling targeted manipulation of individual parts while preserving global consistency. A central global latent further reinforces structural coherence across assembled parts. Our experiments show that the Quartet achieves state-of-the-art performance. To our best knowledge, this is the first 3D point cloud generation framework that fully integrates and enforces both symmetry and part priors throughout the generative process.

Symmetry Analysis

network architecture training
Point cloud airplanes, cars, and chairs with identified symmetry groups and corresponding fundamental domains for each color-coded part. Ref denotes reflection; Rot(𝛼) denotes rotation by angle 𝛼. Our symmetry formulation allows greater flexibility by supporting symmetries composed of multiple transformations, such as two reflections (chair legs (e)) or a rotation followed by a reflection (car wheels). Circular symmetry is approximated via small-angle rotations (chair seat (f)).

Network Architecture

network architecture training
Overview of the Quartet's architecture. Four diffusions are employed to learn the distributions of shape latents, symmetries, parts, and assemblers. By explicitly modeling different distributions, the \ours provides an interpretable and controllable framework to generate high-quality, diverse 3D shapes with guaranteed symmetry. Beige blocks denote learnable modules; gray blocks indicate outputs directly generated from the models.

Results

generation results
Point cloud generation. Samples from the Quartet are visually appealing, diverse, and exhibit strong structural consistency. The last three columns illustrate targeted manipulation.

Citation 

@inproceedings{zhou2023frepolad,
    title={Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance}, 
    author={Chenliang Zhou and Fangcheng Zhong and Weihao Xia and Albert Miao and Canberk Baykal and Cengiz Oztireli},
    booktitle={Proceedings of the International Conference on Learning Representations (ICLR)},
    year={2026}
}


The website template was borrowed from D2NeRF.