Relative Flow Matching for Time-Critical Control in Hardware-Limited Flight

Generative policies are a natural fit for multimodal robot control, but generative sampling can be too expensive for time-critical control on hardware-limited platforms. We introduce Relative Flow Matching (RFM), a reparameterization of flow matching that moves the fixed distribution source towards an action-dependent anchor. This is particularly useful in robotics, where information on prior actions can substantially reduce the transport required between source and consecutive action. By defining the flow in relative coordinates, RFM retains a standard Gaussian source without loss of generality, allowing existing flow-matching objectives and fast samplers to be applied directly. We evaluate RFM on collision-free flight of a morphing-wing drone, where RFM reaches $95.2\pm 1.8$% success in simulation while requiring $4.7$ms per inference on a Raspberry Pi Zero 2W, and transfers to the physical aircraft with 14/15 successful flights. We show that RFM outperforms conventional Flow Matching and other action conditioned methods in terms of performance and speed. Across standard Robomimic and D3IL simulated manipulation benchmarks, RFM improves one-step generation in four of five settings and remains competitive with iterative flow matching at substantially lower inference cost. This work, establishes a continuous connection between standard fixed-source flow matching, stochastic action anchoring, and the deterministic behaviour-cloning boundary. Our results show that RFM's affine reparameterization materially improves very-low-NFE generative control because it changes the conditional source/transport geometry.