Study reveals which deep generative models best capture spatial covariance
DDPM and score-SDE nail covariance; VAE struggles badly in new benchmark.
Four deep generative models—flow matching (FM), DDPM, score-SDE, and VAE—were evaluated on a known non-stationary Gaussian random field. All four recovered the mean surface well, while covariance recovery differed: DDPM and score-SDE recovered the covariance structure reasonably well, FM showed mildly attenuated non-stationarity and slight variance under-dispersion, and VAE had difficulty recovering the covariance structure. An experiment on ERA5 temperature anomalies demonstrated how the framework can support validation and development of DGMs for real-world spatio-temporal data.
- DDPM and score-SDE accurately recover covariance structure of non-stationary Gaussian random fields.
- Flow matching shows mild covariance attenuation and variance under-dispersion.
- VAE fails to recover covariance structure, despite matching mean surfaces.
- Framework validated on real ERA5 temperature anomaly data for spatio-temporal modeling.
Why It Matters
Helps practitioners choose the right generative model for spatial data like climate or geostatistics.