Geometric Constraints in Probabilistic Manifolds: A Bridge from
  Molecular Dynamics to Structured Diffusion Processes
Justin Diamond Markus Lill
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.