Physically Valid Biomolecular Interaction Modeling with Gauss-Seidel Projection

2025-10-09

AI Summary

To address the violation of stereochemical constraints in diffusion-based biomolecular structure generation, this work introduces a differentiable Gauss–Seidel projection module that maps model outputs in real time onto physically feasible conformational manifolds. Leveraging implicit differentiation, the module enables end-to-end training while exploiting the locality and sparsity of molecular constraints to ensure efficient and stable convergence. Remarkably, only two denoising steps suffice to match the structural accuracy of conventional 200-step diffusion models; it achieves comparable SDE/CDR scores across six benchmarks, accelerates inference tenfold, and completely eliminates steric clashes between atoms. The core contribution is the first integration of rigorous, differentiable, and lightweight physical constraints directly into the diffusion generative pipeline—thereby unifying high fidelity, computational efficiency, and structural validity in biomolecular modeling.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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 uniffed module. At its core is a differentiable projection that maps the provisional atom coordinates from the diffusion model to the nearest physically valid conffguration. 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 ffnetuning. With our Gauss-Seidel projection module in place, two denoising steps are sufffcient 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 approximately 10 times faster wall-clock speed while guaranteeing physical validity.

Problem

• Ensuring physical validity in biomolecular interaction modeling
• Correcting steric violations in all-atom structures from foundation models
• Achieving fast convergence with differentiable Gauss-Seidel projection

Innovation

• Differentiable projection enforces physical validity constraints
• Gauss-Seidel scheme ensures fast convergence at scale
• Two-step denoising achieves state-of-the-art accuracy