  AI technology for generating images, such as diffusion models, has advanced
rapidly. However, there is no established framework for quantifying the
reliability of AI-generated images, which hinders their use in critical
decision-making tasks, such as medical image diagnosis. In this study, we
propose a method to quantify the reliability of decision-making tasks that rely
on images produced by diffusion models within a statistical testing framework.
The core concept of our statistical test involves using a selective inference
framework, in which the statistical test is conducted under the condition that
the images are produced by a trained diffusion model. As a case study, we study
a diffusion model-based anomaly detection task for medical images. With our
approach, the statistical significance of medical image diagnostic outcomes can
be quantified in terms of a p-value, enabling decision-making with a controlled
error rate. We demonstrate the theoretical soundness and practical
effectiveness of our statistical test through numerical experiments on both
synthetic and brain image datasets.
