这篇论文对比了DDPM、Score-SDE、FM和VAE在非平稳场上的表现，告诉你哪个模型能更好还原协方差结构，适合关心生成模型统计特性的人。
该论文评估了四种深度生成模型（Flow Matching, DDPM, Score-SDE, VAE）在已知非平稳高斯随机场上的表现。所有四种模型都能恢复均值面，但协方差恢复差异显著：DDPM和Score-SDE效果较好，Flow Matching的非平稳性轻度衰减且方差轻微欠散，VAE难以恢复协方差结构。研究还基于ERA5温度异常数据验证了该评估框架在复杂时空数据中的实用性。
Deep generative models (DGMs) are widely used for complex high-dimensional data and increasingly applied to spatial and spatio-temporal modeling. Their generated samples implicitly represent the learned data distribution and associated uncertainty. However, for real-world data, assessing whether DGMs have learned the underlying process is difficult because the ground truth is unknown and evaluation often relies on observations alone. We evaluate representative DGMs, flow matching (FM), DDPM, score-SDE, and VAE, on a known non-stationary Gaussian random field. This paper provides comprehensive metrics to assess recovery of the ground-truth mean and covariance structures, with oracle samples and a stationary control as references. All four models recover the mean surface, while their covariance recovery differs across model families: DDPM and score-SDE recover the covariance structure reasonably well, FM exhibits mildly attenuated non-stationarity and slight variance under-dispersion, and VAE has difficulty recovering the covariance structure. An experiment on ERA5 temperature anomalies further demonstrates how the framework can support the validation and development of DGMs for complex real-world spatio-temporal data.