Continuous Semantic Navigation Fields for Language-Conditioned Aerial Exploration

Language-conditioned aerial navigation is commonly formulated as next-action prediction over a sparse set of discrete waypoints. This representation discards the feasible intermediate states that determine collision risk, dynamic smoothness, and semantic progress. We introduce CSNF, a Continuous Semantic Navigation Field that treats navigation as conditional probability-flow generation over a continuous trajectory manifold. A multimodal encoder maps language, RGB-D/LiDAR observations, and vehicle state to a semantic-geometric field; a flow-matching transport model then evolves a noise trajectory into a dynamically feasible trajectory while differentiably enforcing occupancy, instruction alignment, and uncertainty constraints. We provide a consistency objective that couples intermediate states to future observations and prove that, under a local regularity assumption, field-based transport has lower discretization bias than vertex-only action policies for the same number of policy evaluations. We evaluate on VLN-CE, Habitat-Matterport3D, and AirSim-style UAV scenes. Extensive real-world UAV flight experiments further validate its robustness, generalization, and practical deployability.