Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes

TL;DR

This paper introduces a method that integrates geometric constraints into diffusion models to enable precise sampling of structured biological and molecular data, enhancing applications like drug design.

Contribution

It presents a novel approach combining constraint projection with diffusion models to sample from constrained distributions in Euclidean spaces.

Findings

Enables sampling from geometrically constrained distributions

Improves precision in molecular and biological complex modeling

Facilitates safer and more targeted drug design

Abstract

Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the state-space, driven either by existing structural knowledge or specific areas of interest within the state-space. We propose a method that enables sampling from distributions that rigorously adhere to arbitrary sets of geometric constraints in Euclidean spaces. This is achieved by integrating a constraint projection operator within the well-regarded architecture of Denoising Diffusion Probabilistic Models, a framework founded in generative modeling and probabilistic inference. The significance of this work becomes apparent, for instance, in the context of deep learning-based drug design, where it is imperative to maintain specific molecular profile interactions to realize the desired therapeutic outcomes and guarantee safety.