SE(3)-Stochastic Flow Matching for Protein Backbone Generation

The computational design of novel protein structures has the potential to impact numerous scientific disciplines greatly. Toward this goal, we introduce FoldFlow, a series of novel generative models of increasing modeling power based on the flow-matching paradigm over $3\mathrm{D}$ rigid motions -- i.e. the group $\text{SE}(3)$ -- enabling accurate modeling of protein backbones. We first introduce FoldFlow-Base, a simulation-free approach to learning deterministic continuous-time dynamics and matching invariant target distributions on $\text{SE}(3)$. We next accelerate training by incorporating Riemannian optimal transport to create FoldFlow-OT, leading to the construction of both more simple and stable flows. Finally, we design FoldFlow-SFM, coupling both Riemannian OT and simulation-free training to learn stochastic continuous-time dynamics over $\text{SE}(3). Our family of FoldFlow, generative models offers several key advantages over previous approaches to the generative modeling of proteins: they are more stable and faster to train than diffusion-based approaches, and our models enjoy the ability to map any invariant source distribution to any invariant target distribution over $\text{SE}(3)$. Empirically, we validate FoldFlow, on protein backbone generation of up to $300$ amino acids leading to high-quality designable, diverse, and novel samples.