Poster
in
Workshop: Deep Generative Model in Machine Learning: Theory, Principle and Efficacy
Probability-Flow ODE in Infinite-Dimensional Function Spaces
Kunwoo Na · Junghyun Lee · Se-Young Yun · Sungbin Lim
Keywords: [ diffusion model ] [ infinite-dimensional function space ] [ function generation ] [ PF-ODE ] [ PDE solving ]
Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such models, we derive, for the first time, an analog of the probability-flow ODE~(PF-ODE) in infinite-dimensional function spaces. Leveraging this newly formulated PF-ODE, we reduce the number of function evaluations while maintaining sample quality in function generation tasks, including applications to PDEs.