  The design of novel protein structures remains a challenge in protein
engineering for applications across biomedicine and chemistry. In this line of
work, a diffusion model over rigid bodies in 3D (referred to as frames) has
shown success in generating novel, functional protein backbones that have not
been observed in nature. However, there exists no principled methodological
framework for diffusion on SE(3), the space of orientation preserving rigid
motions in R3, that operates on frames and confers the group invariance. We
address these shortcomings by developing theoretical foundations of SE(3)
invariant diffusion models on multiple frames followed by a novel framework,
FrameDiff, for learning the SE(3) equivariant score over multiple frames. We
apply FrameDiff on monomer backbone generation and find it can generate
designable monomers up to 500 amino acids without relying on a pretrained
protein structure prediction network that has been integral to previous
methods. We find our samples are capable of generalizing beyond any known
protein structure.
