Data Selection for Conditional Flow Matching via State–Velocity Geometry

Data selection for Conditional Flow Matching (CFM) asks a basic question: *when can one training sample replace another without changing the state-dependent velocity supervision used to learn the flow?* As Flow Matching scales to larger datasets, full-data training becomes increasingly expensive. However, existing data selection methods typically define sample redundancy through static representations or sample-level scores, so samples that appear redundant may still provide distinct supervision for the learned velocity field. Our key insight is that CFM redundancy should be defined by the *state–velocity geometry* of its supervision, with endpoint distance describing zero-order prescribed supervision and local velocity response capturing first-order sensitivity to state changes. Guided by this view, we introduce **State-Jac**, a lightweight one-shot selector that combines endpoint coverage with proxy-based local-response sketches while leaving final CFM training unchanged. Across balanced, long-tailed, and larger-scale paired benchmarks, State-Jac achieves consistent gains in generation quality and rollout fidelity. On CIFAR-10 and ImageNet-100 at a 20% data budget, State-Jac achieves a best-run FID reduction of **9.2%** relative to random selection. On ImageNet-100, its total GPU cost is **24.61%** of that of full-data training.