Probability-Flow ODE in Infinite-Dimensional Function Spaces

• URL: http://arxiv.org/abs/2503.10219v1
• Date: Thu, 13 Mar 2025 10:01:00 GMT
• Title: Probability-Flow ODE in Infinite-Dimensional Function Spaces
• Authors: Kunwoo Na, Junghyun Lee, Se-Young Yun, Sungbin Lim,
• Abstract summary: We derive, for the first time, an analog of the probability-flow ODE (PF-ODE) in infinite-dimensional function spaces.<n>We reduce the number of function evaluations while maintaining sample quality in function generation tasks, including applications to PDEs.
• Score: 26.795793417392037
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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