Title: Imagine That! Leveraging Emergent Affordances for 3D Tool Synthesis. Abstract: In this paper we explore the richness of information captured by the latent space of a vision-based generative model.  The model combines unsupervised generative learning with a task-based performance predictor to learn and to exploit task-relevant object affordances given visual observations from a reaching task, involving a scenario and a stick-like tool.  While the learned embedding of the generative model captures factors of variation in 3D tool geometry (e.g. length, width, and shape), the performance predictor identifies sub-manifolds of the embedding that correlate with task success. Within a variety of scenarios, we demonstrate that traversing the latent space via backpropagation from the performance predictor allows us to imagine tools appropriate for the task at hand.  Our results indicate that affordances – like the utility for reaching – are encoded along smooth trajectories in latent space. Accessing these emergent affordances by considering only high-level performance criteria (such as task success) enables an agent to manipulate tool geometries in a targeted and deliberate way.