Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models

• URL: http://arxiv.org/abs/2501.18863v1
• Date: Fri, 31 Jan 2025 03:10:10 GMT
• Title: Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models
• Authors: Jiaqi Tang, Yuling Yan,
• Abstract summary: This paper contributes to establishing theoretical guarantees for the probability flow ODE, a diffusion-based sampler known for its practical efficiency. We demonstrate that, with accurate score function estimation, the probability flow ODE sampler achieves a convergence rate of $O(k/T)$ in total variation distance. This dimension-free convergence rate improves upon existing results that scale with the typically much larger ambient dimension.
• Score: 5.064404027153094
• License:
• Abstract: Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability flow ODE, a widely used diffusion-based sampler known for its practical efficiency. While a number of prior works address its general convergence theory, it remains unclear whether the probability flow ODE sampler can adapt to the low-dimensional structures commonly present in natural image data. We demonstrate that, with accurate score function estimation, the probability flow ODE sampler achieves a convergence rate of $O(k/T)$ in total variation distance (ignoring logarithmic factors), where $k$ is the intrinsic dimension of the target distribution and $T$ is the number of iterations. This dimension-free convergence rate improves upon existing results that scale with the typically much larger ambient dimension, highlighting the ability of the probability flow ODE sampler to exploit intrinsic low-dimensional structures in the target distribution for faster sampling.

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