ImpactFlow: Guiding Flow Matching with Geometry from Future Outcomes

Generative models are trained through local prediction signals, yet their quality is judged on completed outputs. Under limited capacity and computation, how should learning prioritize local errors according to their future consequences? In flow matching, equal-norm velocity errors receive equal local cost even when the remaining dynamics carry them into different output changes. We introduce **terminal-transported residual geometry**, which relates error directions at the current state to their predicted effects after the remaining generation process. Output structure specifies which changes matter, and the remaining dynamics determine how local directions contribute to those changes. **ImpactFlow** instantiates this view as directional residual weighting for flow matching, preserving the original conditional velocity labels and the deployment interface. Experiments on low-step HumanML3D text-to-motion generation show that transported geometry predicts independently measured output changes better than decoder-only geometry. Controlled training comparisons demonstrate improved generation quality over endpoint geometry after matching scalar training strength, supporting directional future impact as an effective learning signal. These results support a learning principle: local errors should be prioritized by their future impact on the generated outcome.