Symmetry Matters: Auditing and Symmetrizing 3D Generative Models

TL;DR

This paper investigates symmetry preservation in 3D point cloud generative models, revealing a gap in symmetry encoding and proposing a data-centric intervention to improve geometric consistency.

Contribution

It introduces a symmetry-aware evaluation protocol, analyzes symmetry dynamics during training, and proposes a simple yet effective data-centric method to enhance symmetry in generated 3D shapes.

Findings

Current models show a symmetry gap under symmetry-aware evaluation.

Training on half-objects and reflection during sampling improves symmetry.

Symmetry-aware evaluation and interventions enhance geometric plausibility.

Abstract

Symmetry is a strong prior present in many object categories, yet standard benchmarks for 3D generative models rarely report whether this prior is preserved. We study symmetry preservation in unconditional point cloud generation. We first audit the symmetry of generated shapes by several 3D generative models and compute a normalized symmetry score based on the Chamfer Distance (CD). We show that although current 3D generative models achieve competitive results under standard evaluation, they reveal a persistent symmetry gap when a symmetry-aware evaluation protocol is applied. To test whether this gap is merely inherited from the training data, we evaluate these models over a mirrored-objects dataset derived from ShapeNet and analyze symmetry dynamics during training. Mechanistic interpretability techniques were employed at the sampling and latent levels to further show that reflection symmetry is not reliably encoded in the learned generative process. Finally, to address this gap, we propose a data-centric symmetry-aware intervention: training generative models on a half-objects dataset and reconstructing full objects by reflection during sampling. Across multiple backbones, this intervention substantially improves geometric consistency and visual plausibility while remaining competitive under standard metrics. These findings suggest that symmetry-aware evaluation is needed alongside standard benchmarks, and incoming 3D generative models should incorporate this prior explicitly, either during training or sampling.