A theory of learning data statistics in diffusion models, from easy to hard
While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images exhibit a distributional simplicity bias, learning simple, pair-wise input statistics before specializing to higher-order correlations. We reproduce this behaviour in simple denoisers trained on a minimal data model, the mixed cumulant model, where we precisely control both pair-wise and higher-order correlations of the inputs. We identify a scalar invariant of the model that governs the sample complexity of learning pair-wise and higher-order correlations ...
| Authors | Lorenzo Bardone, Claudia Merger, Sebastian Goldt |
|---|---|
| Primary category | stat.ML |
| Published | 13 March 2026 |
| Last updated at source | 10 June 2026 |
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