Probability-Flow ODE in Infinite-Dimensional Function Spaces

Kunwoo Na, Junghyun Lee, Se-Young Yun, Sungbin Lim

Track: long paper (up to 8 pages)

Keywords: diffusion model, PF-ODE, infinite-dimensional function space, function generation, PDE solving

TL;DR: We derive an analog of the probability-flow ODE in infinite-dimensional function spaces and accelerate the inference procedure in function generation tasks.

Abstract: 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.

Submission Number: 93