Understanding fine-grained object affordances is imperative for robots to manipulate objects in unstructured environments given open-ended task instructions. However, existing methods of visual affordance predictions often rely on manually annotated data or conditions only on a predefined set of tasks. We introduce UAD (Unsupervised Affordance Distillation), a method for distilling affordance knowledge from foundation models into a task-conditioned affordance model without any manual annotations. By leveraging the complementary strengths of large vision models and vision-language models, UAD automatically annotates a large-scale dataset with detailed $<$instruction, visual affordance$>$ pairs. Training only a lightweight task-conditioned decoder atop frozen features, UAD exhibits notable generalization to in-the-wild robotic scenes and to various human activities, despite only being trained on rendered objects in simulation. Using affordance provided by UAD as the observation space, we show an imitation learning policy that demonstrates promising generalization to unseen object instances, object categories, and even variations in task instructions after training on as few as 10 demonstrations. Project website: https://unsup-affordance.github.io/