Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection

Biomolecular interaction modeling has been substantially advanced by foundation models, yet they often produce all-atom structures that violate basic steric feasibility. We address this limitation by enforcing physical validity as a strict constraint during both training and inference with a unified module. At its core is a differentiable projection that maps the provisional atom coordinates from the diffusion model to the nearest physically valid configuration. This projection is achieved using a Gauss-Seidel scheme, which exploits the locality and sparsity of the constraints to ensure stable and fast convergence at scale. By implicit differentiation to obtain gradients, our module integrates seamlessly into existing frameworks for end-to-end finetuning. With our Gauss-Seidel projection module in place, two de-noising steps are sufficient to produce biomolecular complexes that are both physically valid and structurally accurate. Across six benchmarks, our 2-step model achieves the same structural accuracy as state-of-the-art 200-step diffusion baselines, delivering 10 wall-clock speedups while guaranteeing physical validity. End-to-end, all-atom protein structure predictors that integrate deep learning with generative modeling are emerging as transformative tools for biomolecular interaction modeling (Senior et al., 2020b; Jumper et al., 2021; Abramson et al., 2024; Corso et al., 2023; Watson et al., 2023). These systems achieve unprecedented accuracy in predicting arbitrary biomolecular complexes and are shaping the future of computational biology and drug discovery. Contrary to their high structural accuracy, current predictors often fail to satisfy a conceptually simpler but basic requirement: the physical validity of the all-atom output. This failure, also commonly termed hallucination, appears as steric clashes, distorted covalent geometry, and stereochemical errors (Figure 1).