Collision Avoidance and Shape Fidelity in Flow-Based Swarm Formation

Collision avoidance and shape fidelity impose distinct requirements on flow-based swarm formation. We study their relationship using a frozen conditional flow-matching model. On airplane and car, learned second-order corrections with selected damping do not significantly outperform first-order controls. Across training seeds of potential-based corrections, models that produce more collision-free rollouts also place agents farther from the generated reference surface. Two loss interventions alter geometric deviation and collision performance without eliminating close contacts. We then construct a fixed pairwise correction from empirical distance statistics and integrate it with a displacement cap and adaptive sub-steps. Without retraining, it achieves 500 clean rollouts out of 500 across five agent counts up to 512 in each of five ShapeNet categories. Optimal reciprocal collision avoidance, applied within the sampling loop at its released settings, matches these collision counts, but the methods differ in their effects on formation geometry. Ablations show that integration controls affect collision performance and that similar collision counts can accompany substantially different geometric errors.