Compositional generative modeling proposes that complex generative systems should be built by combining simpler models rather than relying on single large models. This approach enables more data-efficient learning, better generalization to unseen data, and the ability to construct new models for previously unseen tasks. The paper argues that while large generative models have become dominant in AI research, they are limited in scalability, cost, and adaptability. Compositional models, by contrast, can be built from smaller components that capture subsets of variables, allowing for more efficient learning and generalization. The paper demonstrates that compositional models can be more data-efficient, as they can learn simpler distributions with fewer parameters and less data. They also enable the creation of new models for tasks not seen during training, by combining existing components. Furthermore, compositional structures can be discovered from data, allowing for the creation of new distributions by recombining discovered components. The paper illustrates the benefits of compositional generative modeling across various domains, including trajectory modeling, visual generation, and language modeling. It shows that compositional models can generate more accurate results with less data and can be more flexible in adapting to new tasks. The paper also discusses the challenges of implementing compositional sampling, particularly with common generative model parameterizations, and presents methods for effective compositional sampling in both continuous and discrete domains. Finally, the paper discusses the broader implications of compositional generative modeling, including its potential for more efficient and interpretable systems, as well as its environmental and deployment benefits. It also highlights the need for future research to address limitations, such as the need for automatic discovery of compositional structures and the development of more robust methods for discovering compositional structures in real-world data.Compositional generative modeling proposes that complex generative systems should be built by combining simpler models rather than relying on single large models. This approach enables more data-efficient learning, better generalization to unseen data, and the ability to construct new models for previously unseen tasks. The paper argues that while large generative models have become dominant in AI research, they are limited in scalability, cost, and adaptability. Compositional models, by contrast, can be built from smaller components that capture subsets of variables, allowing for more efficient learning and generalization. The paper demonstrates that compositional models can be more data-efficient, as they can learn simpler distributions with fewer parameters and less data. They also enable the creation of new models for tasks not seen during training, by combining existing components. Furthermore, compositional structures can be discovered from data, allowing for the creation of new distributions by recombining discovered components. The paper illustrates the benefits of compositional generative modeling across various domains, including trajectory modeling, visual generation, and language modeling. It shows that compositional models can generate more accurate results with less data and can be more flexible in adapting to new tasks. The paper also discusses the challenges of implementing compositional sampling, particularly with common generative model parameterizations, and presents methods for effective compositional sampling in both continuous and discrete domains. Finally, the paper discusses the broader implications of compositional generative modeling, including its potential for more efficient and interpretable systems, as well as its environmental and deployment benefits. It also highlights the need for future research to address limitations, such as the need for automatic discovery of compositional structures and the development of more robust methods for discovering compositional structures in real-world data.