Data Manifold

Data manifolds represent the underlying low-dimensional structure of high-dimensional datasets, aiming to capture the intrinsic geometry and relationships within the data. Current research focuses on developing generative models, such as diffusion models and normalizing flows, that operate directly on these manifolds, often leveraging techniques like Riemannian geometry and isometric learning to preserve the data's inherent structure. This work has significant implications for various fields, improving generative modeling, enhancing model explainability, and enabling robust analysis of complex datasets in applications ranging from drug discovery to image generation and anomaly detection.