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.

翻译：理解生物复合体的宏观特性需要统计系综建模的精确性与特异性。该领域的主要挑战之一在于从状态空间的特定子集中进行采样，这种需求源于现有的结构知识或对状态空间中特定区域的关注。我们提出了一种方法，能够从严格满足欧几里得空间中任意几何约束集的分布中进行采样。这是通过将约束投影算子集成到去噪扩散概率模型这一成熟的生成建模与概率推理框架中实现的。本研究的意义在深度学习驱动的药物设计中尤为凸显——在该领域，维持特定的分子谱相互作用对于实现预期治疗效果并保障安全性至关重要。