Abstract
Synthetic data can scale visual pretraining, but current selection criteria only partially explain which datasets train strong representations. We propose using the energy profile of a dataset--the distribution of log-probability levels it occupies under a normalised real-image density model--as an audit and curation principle for synthetic data.
To operationalise this view, we introduce Energy-Level Distribution Distance (ELD), which compares real and synthetic energy distributions. Real images span sparse high-likelihood scenes and dense low-likelihood textures, so useful synthetic data should cover this energy range rather than collapse to likely but low-variation samples.
Across diverse synthetic datasets, ELD exposes mismatches missed by FID and predicts pretraining performance beyond FID, LPIPS variation, and feature-space recall, including across CNN and ViT self-supervised settings. We then use ELD to resample and mix synthetic sources, matching the real-image energy histogram while preserving diversity and improving downstream transfer.