Symmetry-Aware Generative Modeling through Learned Canonicalization

Kusha Sareen, Daniel Levy, Arnab Kumar Mondal, Sékou-Oumar Kaba, Tara Akhound-Sadegh, Siamak Ravanbakhsh

Keywords: Generative modeling, equivariance, symmetry, deep learning.

TL;DR: We propose a generative modeling framework that uses learned canonicalization to project a distribution on its orbits, enabling the use of non-equivariant models for faster and more flexible generation while maintaining high sample quality.

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.

Submission Number: 67