The paper develops a theoretical framework to understand the phenomenon of *critical windows* in diffusion models for image generation. Critical windows refer to narrow time intervals during which specific features of the final image emerge, such as the class or background color. The authors propose a formal framework to study these windows and show that for data coming from a mixture of strongly log-concave densities, these windows can be bounded in terms of certain measures of inter- and intra-group separation. They provide concrete bounds for specific distribution classes, such as well-conditioned Gaussian mixtures, and use these bounds to interpret diffusion models as hierarchical samplers that progressively "decide" output features over a discrete sequence of times. The theoretical findings are validated through synthetic experiments, and preliminary results on Stable Diffusion suggest that critical windows may serve as a useful tool for diagnosing fairness and privacy violations in real-world diffusion models.The paper develops a theoretical framework to understand the phenomenon of *critical windows* in diffusion models for image generation. Critical windows refer to narrow time intervals during which specific features of the final image emerge, such as the class or background color. The authors propose a formal framework to study these windows and show that for data coming from a mixture of strongly log-concave densities, these windows can be bounded in terms of certain measures of inter- and intra-group separation. They provide concrete bounds for specific distribution classes, such as well-conditioned Gaussian mixtures, and use these bounds to interpret diffusion models as hierarchical samplers that progressively "decide" output features over a discrete sequence of times. The theoretical findings are validated through synthetic experiments, and preliminary results on Stable Diffusion suggest that critical windows may serve as a useful tool for diagnosing fairness and privacy violations in real-world diffusion models.