Infinite Dimensional

Research on infinite-dimensional spaces focuses on developing and analyzing models and algorithms that operate directly on functions or data residing in such spaces, rather than relying on finite-dimensional approximations. Current efforts concentrate on adapting diffusion models, particularly score-based methods, to infinite-dimensional settings, often employing neural operators or function-space conditioning techniques to handle the complexities of high-dimensional data like images and time series. This work is significant because it addresses limitations of finite-dimensional approaches, offering improved scalability, generalization, and the potential for more accurate and efficient modeling of complex systems in various scientific and engineering domains.