The computational design of novel protein structures has the potential to
impact numerous scientific disciplines greatly. Toward this goal, we introduce
$\text{FoldFlow}$ a series of novel generative models of increasing modeling
power based on the flow-matching paradigm over $3\text{D}$ rigid motions --
i.e. the group $\text{SE(3)}$ -- enabling accurate modeling of protein
backbones. We first introduce $\text{FoldFlow-Base}$, 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 $\text{FoldFlow-OT}$,
leading to the construction of both more simple and stable flows. Finally, we
design $\text{FoldFlow-SFM}$ coupling both Riemannian OT and simulation-free
training to learn stochastic continuous-time dynamics over $\text{SE(3)}$. Our
family of $\text{FoldFlow}$ generative models offer 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 our FoldFlow
models on protein backbone generation of up to $300$ amino acids leading to
high-quality designable, diverse, and novel samples.

FoldFlow 是一系列基于流匹配范式的新型生成模型，通过流动匹配 3D 刚体运动（即群 SE (3)），实现对蛋白质主链的准确建模，具备比其他方法更稳定、更快速的训练能力，并可以将任何不变的源分布映射到 SE (3) 上的任何不变的目标分布。