2025/12/01 by Debaussart-Joniec, Gwendal, Kalogeratos, Argyris
Computer Science · Mathematics · #Artificial Intelligence (cs.AI) #Cluster analysis #Degrees of freedom (physics and chemistry) #Diffusion #Diffusion map #Diffusion process #Ergodicity #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Medical Image Segmentation Techniques #Morphological variations and asymmetry #Operator (biology) #Probabilistic logic #Topological and Geometric Data Analysis
paper · open access · doi:10.48550/arxiv.2512.01484
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the random walk operators of multiple data views. Each MDT defines a trajectory-dependent diffusion operator with a clear probabilistic and geometric interpretation, capturing over time the interplay between data views. Our formulation encompasses existing multi-view diffusion models, while providing new degrees of freedom for view interaction and fusion. We establish theoretical properties under mild assumptions, including ergodicity of both the point-wise operator and the process in itself. We also derive MDT-based diffusion distances, and associated embeddings via singular value decompositions. Finally, we propose various strategies for learning MDT operators within the defined operator space, guided by internal quality measures. Beyond enabling flexible model design, MDTs also offer a neutral baseline for evaluating diffusion-based approaches through comparison with randomly selected MDTs. Experiments show the practical impact of the MDT operators in a manifold learning and data clustering context.