Dense greenhouse-gas (GHG) observations, particularly from satellites, require fast atmospheric transport models that link surface emissions to these observations. We introduce GenGHG, a generative machine learning (ML) model that emulates footprints from the Stochastic Time-Inverted Lagrangian Transport (STILT) model. These footprints estimate how a unit of emissions would alter a downwind atmospheric measurement. Unlike existing deterministic ML emulators, which give a single prediction, GenGHG predicts an ensemble of plausible footprints under given meteorological forcing conditions to represent stochastic atmospheric transport. GenGHG retains ML-level computational efficiency, with each member generated in less than 2 s on a single GPU, and we evaluate its generative advantage over deterministic ML across a benchmark of 60 urban areas worldwide. Results show that GenGHG preserves footprint total mass substantially better than deterministic ML, with a mean relative bias of +2.67 % compared with −22.38 %, and also better preserves the footprint-value distribution. Grid-level accuracy also shows that GenGHG better captures spatial footprint patterns, with larger gains in more dispersive transport regimes. We further test GenGHG’s advantage in a synthetic inverse modeling experiment, where transport from GenGHG yields methane emission estimates that closely follow the STILT transport reference and outperform deterministic ML. Finally, we highlight GenGHG’s compatibility with any global meteorology product at a 0.25° resolution. This flexibility, combined with its low computational cost, makes it straightforward to run footprints using multiple meteorology products and subsequently evaluate the possible effects of meteorological uncertainties.