Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models
This provides theoretical guarantees for faster sampling in generative AI by exploiting intrinsic data structures, though it is incremental as it builds on prior convergence theory.
The paper tackles the problem of whether the probability flow ODE sampler in diffusion generative models can adapt to low-dimensional structures in data, and demonstrates that with accurate score estimation, it achieves a convergence rate of O(k/T) in total variation distance, where k is the intrinsic dimension, improving over rates scaling with ambient dimension.
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.