Constrained Sampling of Discrete Geometric Manifolds using Denoising Diffusion Probabilistic Models

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 discrete 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 sample from the discrete structures of the solution space.