Probability-Flow ODE in Infinite-Dimensional Function Spaces

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.

@article{na2025_2503.10219,
  title={ Probability-Flow ODE in Infinite-Dimensional Function Spaces },
  author={ Kunwoo Na and Junghyun Lee and Se-Young Yun and Sungbin Lim },
  journal={arXiv preprint arXiv:2503.10219},
  year={ 2025 }
}