Achieving complex, long-horizon robot behavior remains challenging because successful execution depends on skills grounded in a robot's physical affordances. Existing training-task distributions are often handcrafted or sampled from large language models (LLMs), relying on semantic plausibility rather than embodiment-specific feasibility. This mismatch can produce curricula that are too difficult, redundant, or blind to non-obvious but learnable behaviors. We propose Generative Flow on Symbolic Abstractions (FOSA), a framework for discovering embodiment-specific capabilities by learning a grounded task generator. FOSA parameterizes an abstract policy as a Generative Flow Network that constructs symbolic task skeletons. Each skeleton is compiled into a simulation environment, where low-level policy-learning performance provides the reward signal for the abstract policy. Across heterogeneous robot platforms, FOSA discovers diverse and executable tasks near the robot's empirical capability frontier. After distilling the discovered task policies into a single language-conditioned policy, FOSA improves performance on unseen complex and long-horizon tasks. The code and demonstration videos are available at https://www.youwei-yu.com/fosa.

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