Steric Hamiltonian Flows for Proteins

Proteins are central to nearly all biological processes, and their diverse functions arise from their complex 3D structures. Recent advances in deep learning have transformed this field, with diffusion-based generative models revolutionizing protein design by enabling the creation of novel protein structures. However, these methods lack physical inductive biases and neglect the intrinsic physical realism of proteins, driven by noising dynamics that lack grounding in physical principles. To address this, we first introduce a physically motivated structured noising process, grounded in classical physics, that unfolds proteins into secondary structures (e.g., $\alpha$-helices, linear $\beta$-sheets) while maintaining bonds and preventing collisions. We integrate this process with $\mathrm{SE}(3)$ flow-matching to model protein backbone distributions while incorporating sequence information for conditional folding. Our method outperforms baselines trained on the same dataset and matches those trained on substantially larger ones across short- and long-chain generation, and motif-scaffolding tasks.