Diffusion models have emerged as a leading generative modeling technique, demonstrating strong performance in image synthesis and other modalities. They are unique in that they do not require labeled data, making them suitable for self-supervised learning. This survey explores the relationship between diffusion models and representation learning, providing an overview of their mathematical foundations, denoising network architectures, and guidance methods. It details various approaches that leverage pre-trained diffusion models for downstream tasks and methods that enhance diffusion models using representation learning. The survey aims to provide a comprehensive taxonomy of these approaches, identifying key areas of research and potential future directions. Diffusion models work by gradually adding noise to images and then learning to reverse this process. They are trained to predict the noise added at each step, enabling the generation of new images. The process involves a denoising network that learns to remove noise from images, with the network's parameters being trained to minimize the difference between predicted and actual noise. This training process is based on a variational lower bound of the negative log-likelihood. The survey discusses various architectures used in diffusion models, including U-Net and transformer-based models like DiT. These architectures are used to approximate the score function and enable the generation of high-quality images. The paper also covers different guidance methods, such as classifier guidance and classifier-free guidance, which allow for controlled generation by incorporating user-defined conditions. In terms of representation learning, diffusion models can be used to learn semantic features that are useful for downstream tasks like segmentation and classification. The paper outlines methods that extract intermediate activations from diffusion models for these tasks, showing that these features can be used to achieve competitive performance in tasks like image classification and semantic segmentation. The survey also discusses the use of diffusion models for correspondence tasks, where the goal is to find corresponding points between images. Overall, the survey highlights the potential of diffusion models in representation learning, showing that they can learn meaningful features that are useful for a wide range of downstream tasks. The paper provides a comprehensive overview of the current state of research, identifying key areas of interest and potential future directions in the field.Diffusion models have emerged as a leading generative modeling technique, demonstrating strong performance in image synthesis and other modalities. They are unique in that they do not require labeled data, making them suitable for self-supervised learning. This survey explores the relationship between diffusion models and representation learning, providing an overview of their mathematical foundations, denoising network architectures, and guidance methods. It details various approaches that leverage pre-trained diffusion models for downstream tasks and methods that enhance diffusion models using representation learning. The survey aims to provide a comprehensive taxonomy of these approaches, identifying key areas of research and potential future directions. Diffusion models work by gradually adding noise to images and then learning to reverse this process. They are trained to predict the noise added at each step, enabling the generation of new images. The process involves a denoising network that learns to remove noise from images, with the network's parameters being trained to minimize the difference between predicted and actual noise. This training process is based on a variational lower bound of the negative log-likelihood. The survey discusses various architectures used in diffusion models, including U-Net and transformer-based models like DiT. These architectures are used to approximate the score function and enable the generation of high-quality images. The paper also covers different guidance methods, such as classifier guidance and classifier-free guidance, which allow for controlled generation by incorporating user-defined conditions. In terms of representation learning, diffusion models can be used to learn semantic features that are useful for downstream tasks like segmentation and classification. The paper outlines methods that extract intermediate activations from diffusion models for these tasks, showing that these features can be used to achieve competitive performance in tasks like image classification and semantic segmentation. The survey also discusses the use of diffusion models for correspondence tasks, where the goal is to find corresponding points between images. Overall, the survey highlights the potential of diffusion models in representation learning, showing that they can learn meaningful features that are useful for a wide range of downstream tasks. The paper provides a comprehensive overview of the current state of research, identifying key areas of interest and potential future directions in the field.