Symmetry-Aware Generative Modeling through Learned Canonicalization

TL;DR

This paper introduces a symmetry-aware generative modeling approach that learns canonical representations to improve sample quality and inference speed, avoiding limitations of traditional equivariant methods.

Contribution

It proposes a learned canonicalization network to map symmetric data to a canonical form, enabling non-equivariant generative models to better handle symmetries.

Findings

Improved sample quality in molecular modeling.

Faster inference times compared to existing methods.

Promising preliminary experimental results.

Abstract

Generative modeling of symmetric densities has a range of applications in AI for science, from drug discovery to physics simulations. The existing generative modeling paradigm for invariant densities combines an invariant prior with an equivariant generative process. However, we observe that this technique is not necessary and has several drawbacks resulting from the limitations of equivariant networks. Instead, we propose to model a learned slice of the density so that only one representative element per orbit is learned. To accomplish this, we learn a group-equivariant canonicalization network that maps training samples to a canonical pose and train a non-equivariant generative model over these canonicalized samples. We implement this idea in the context of diffusion models. Our preliminary experimental results on molecular modeling are promising, demonstrating improved sample quality and faster inference time.