Accurately estimating greenhouse gas (GHG) emissions from atmospheric observations requires resolving the upwind influence of measurements via atmospheric transport models. However, the computational demands of full-physics models limit the scalability of flux inversions, particularly for dense in situ and satellite-based observations. Here, we present FootNet v3, a deep-learning emulator of atmospheric transport based on a U-Net++ architecture, which improves generalization and inversion fidelity over prior U-Net-based models. FootNet v3 is trained on 500,000 pseudo-observations across the contiguous United States. It predicts surface and column-averaged source-receptor relationships at kilometer-scale resolution and operates 650x faster than traditional Lagrangian models. Critically, FootNet learns the underlying physical relationship between meteorology and atmospheric transport. We show that it accurately predicts source-receptor relationships when driven by GFS meteorology, despite being trained on HRRR data. FootNet generalizes to unseen regions and meteorological regimes, enabling accurate flux inversions in domains withheld during training. Case studies using GHG measurements in the San Francisco Bay Area and Barnett Shale show that FootNet matches or exceeds the performance of full-physics models when evaluated against independent GHG observations. This is achieved despite FootNet having never seen meteorological inputs from Northern California or North Texas. Feature importance testing identifies physically meaningful drivers that are consistent across both surface and column models. These findings show that machine learning models can learn the physics governing atmospheric transport, allowing them to extrapolate to out-of-sample scenarios and support real-time, high-resolution GHG flux estimation in novel domains without the need for retraining or precomputed footprint libraries.