Provable Efficiency of Guidance in Diffusion Models for General Data Distribution

Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only focus on case studies, where the distribution conditioned on each class is either isotropic Gaussian or supported on a one-dimensional interval with some extra conditions. How to analyze the guidance effect beyond these case studies remains an open question. Towards closing this gap, we make an attempt to analyze diffusion guidance under general data distributions. Rather than demonstrating uniform sample quality improvement, which does not hold in some distributions, we prove that guidance can improve the whole sample quality, in the sense that the ratio of bad samples (measured by the classifier probability) decreases in the presence of guidance. This aligns with the motivation of introducing guidance.

Diffusion models are a new type of artificial intelligence tool that can generate realistic images, text, or other data. To make the generated results more accurate or aligned with a goal—like drawing a specific kind of animal—researchers often add something called guidance to steer the model in the right direction. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only focus on some simple situations, which don't reflect the wide variety of data we see in the real world. Towards closing this gap, we make an attempt to analyze diffusion guidance under general data distributions. Rather than demonstrating uniform sample quality improvement, which does not hold in some distributions, we prove that guidance can improve the whole sample quality, in the sense that the ratio of bad samples (measured by the classifier probability) decreases in the presence of guidance. This aligns with the motivation of introducing guidance.