A Mesh Is Worth 512 Numbers: Spectral-domain Diffusion Modeling for High-dimension Shape Generation

Recent advancements in learning latent codes derived from high-dimensional shapes have demonstrated impressive outcomes in 3D generative modeling. Traditionally, these approaches employ a trained autoencoder to acquire a continuous implicit representation of source shapes, which can be computationally expensive. This paper introduces a novel framework, spectral-domain diffusion for high-quality shape generation SpoDify, that utilizes singular value decomposition (SVD) for shape encoding. The resulting eigenvectors can be stored for subsequent decoding, while generative modeling is performed on the eigenfeatures. This approach efficiently encodes complex meshes into continuous implicit representations, such as encoding a 15k-vertex mesh to a 512-dimensional latent code without learning. Our method exhibits significant advantages in scenarios with limited samples or GPU resources. In mesh generation tasks, our approach produces high-quality shapes that are comparable to state-of-the-art methods.

Enhancing Plausibility Evaluation for Generated Designs with Denoising Autoencoder

A great interest has arisen in using Deep Generative Models (DGM) for generative design. When assessing the quality of the generated designs, human designers focus more on structural plausibility, e.g., no missing component, rather than visual artifacts, e.g., noises in the images. Meanwhile, commonly used metrics such as Fr\'echet Inception Distance (FID) may not evaluate accurately as they tend to penalize visual artifacts instead of structural implausibility. As such, FID might not be suitable to assess the performance of DGMs for a generative design task. In this work, we propose to encode the input designs with a simple Denoising Autoencoder (DAE) and measure the distribution distance in the latent space thereof. We experimentally test our DAE-based metrics with FID and other state-of-the-art metrics on three data sets: compared to FID and some more recent works, e.g., FD$_\text{DINO-V2}$ and topology distance, DAE-based metrics can effectively detect implausible structures and are more consistent with structural inspection by human experts.