The paper advocates for a compositional approach to generative modeling, where complex models are constructed by combining simpler, smaller models. This method is argued to be more data-efficient and computationally efficient compared to training large monolithic models. The authors demonstrate that compositional models can generalize to unseen parts of the data distribution and can be programmed to handle new tasks without explicit fine-tuning. They also show that compositional components can often be discovered from raw data, making the process more flexible and interpretable. The paper discusses the benefits of compositional models in various domains, including trajectory modeling, visual synthesis, and hierarchical planning. Additionally, it explores the challenges and practical implementations of compositional sampling, particularly in continuous and discrete spaces. The authors conclude by highlighting the potential of compositional models in building decentralized decision-making systems and their broader impact in AI applications.The paper advocates for a compositional approach to generative modeling, where complex models are constructed by combining simpler, smaller models. This method is argued to be more data-efficient and computationally efficient compared to training large monolithic models. The authors demonstrate that compositional models can generalize to unseen parts of the data distribution and can be programmed to handle new tasks without explicit fine-tuning. They also show that compositional components can often be discovered from raw data, making the process more flexible and interpretable. The paper discusses the benefits of compositional models in various domains, including trajectory modeling, visual synthesis, and hierarchical planning. Additionally, it explores the challenges and practical implementations of compositional sampling, particularly in continuous and discrete spaces. The authors conclude by highlighting the potential of compositional models in building decentralized decision-making systems and their broader impact in AI applications.