Instance-dependent Convergence Theory for Diffusion Models

Understand

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions.

• Improving the theoretical understanding of diffusion models, with a particular focus on the convergence analysis, has attracted significant attention.
• In this work, we develop a convergence rate that is adaptive to the smoothness of different target distributions, referred to as instance-dependent bound.
• Specifically, we establish an iteration complexity of $\min\{d,d^{2/3}L^{1/3},d^{1/3}L\}\varepsilon^{-2/3}$ (up to logarithmic factors), where $d$ denotes the data dimension, and $\varepsilon$ quantifies the output accuracy in terms of total variation (TV) distance.