Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes
This work addresses the need for precise sampling in domains like drug design, where maintaining specific molecular interactions is crucial for therapeutic outcomes and safety.
The paper tackles the challenge of sampling from specific subsets of state-spaces, such as in molecular dynamics, by proposing a method that integrates geometric constraints into Denoising Diffusion Probabilistic Models to enable sampling from distributions adhering to arbitrary constraints.
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.