This paper investigates the hierarchical nature of data through the lens of diffusion models, revealing a phase transition in the denoising process. The study focuses on a hierarchical generative model of data, inspired by formal grammar and statistical physics, to understand how diffusion models capture the structure of real-world data. The key finding is that during the backward diffusion process, the probability of reconstructing high-level features, such as the class of an image, drops suddenly at a threshold time, while low-level features evolve smoothly. This implies that after the phase transition, the class may have changed, but the generated sample may still retain low-level elements from the original image. The study validates these insights through numerical experiments on class-unconditional ImageNet diffusion models. It characterizes the relationship between time and scale in diffusion models and highlights the potential of generative models to model combinatorial data properties. The analysis shows that diffusion models operate at different hierarchical levels of the data at different time scales within the diffusion process. The results are supported by empirical observations, including the behavior of hidden representations in deep networks, which align with the theoretical predictions. The paper introduces a hierarchical generative model of data, which mimics the hierarchical and compositional structure of images. It demonstrates that the denoising process in diffusion models can be solved exactly for this model using belief propagation. The analysis reveals a phase transition at a critical noise value, where the probability of remaining in the same class drops suddenly. This phase transition is confirmed through both theoretical analysis and numerical experiments on synthetic and real data. The study also explores the implications of this phase transition for understanding the success of diffusion models, including their ability to generalize and avoid memorization of training data. The findings suggest that diffusion models can effectively capture the hierarchical structure of data, making them powerful tools for generating complex, structured data. The results are consistent across different data types, including images and text, indicating that the phase transition phenomenon is a general property of diffusion models.This paper investigates the hierarchical nature of data through the lens of diffusion models, revealing a phase transition in the denoising process. The study focuses on a hierarchical generative model of data, inspired by formal grammar and statistical physics, to understand how diffusion models capture the structure of real-world data. The key finding is that during the backward diffusion process, the probability of reconstructing high-level features, such as the class of an image, drops suddenly at a threshold time, while low-level features evolve smoothly. This implies that after the phase transition, the class may have changed, but the generated sample may still retain low-level elements from the original image. The study validates these insights through numerical experiments on class-unconditional ImageNet diffusion models. It characterizes the relationship between time and scale in diffusion models and highlights the potential of generative models to model combinatorial data properties. The analysis shows that diffusion models operate at different hierarchical levels of the data at different time scales within the diffusion process. The results are supported by empirical observations, including the behavior of hidden representations in deep networks, which align with the theoretical predictions. The paper introduces a hierarchical generative model of data, which mimics the hierarchical and compositional structure of images. It demonstrates that the denoising process in diffusion models can be solved exactly for this model using belief propagation. The analysis reveals a phase transition at a critical noise value, where the probability of remaining in the same class drops suddenly. This phase transition is confirmed through both theoretical analysis and numerical experiments on synthetic and real data. The study also explores the implications of this phase transition for understanding the success of diffusion models, including their ability to generalize and avoid memorization of training data. The findings suggest that diffusion models can effectively capture the hierarchical structure of data, making them powerful tools for generating complex, structured data. The results are consistent across different data types, including images and text, indicating that the phase transition phenomenon is a general property of diffusion models.