Large Diffusion Models Need More Than EMA

Large-scale diffusion models are commonly trained with a constant learning rate (LR) and exponential moving average (EMA), despite the strong performance of LR decay and Schedule-Free optimization in training large language models. We study whether EMA is uniquely suited to diffusion training, or whether stronger alternatives have been underexplored. Through the lens of variance reduction, we theoretically show that averaging a constant-step trajectory has an inherent optimization limitation, whereas LR decay and Schedule-Free optimization admit vanishing stationarity guarantees under standard nonconvex assumptions. Empirically, LR decay and EMA provide complementary rather than substitutable benefits: decay alone does not outperform EMA with a constant LR, while combining decay with EMA further improves this standard baseline at most tested starting points, although the gain remains sensitive to when decay begins. Schedule-Free avoids this timing requirement and consistently outperforms EMA with a constant LR across training stages, achieving both lower fixed-evaluation objectives and better generation quality. Our analysis further shows that all three strategies substantially reduce parameter variability, yet stronger stabilization is not always better: EMA with a constant LR retains comparatively higher parameter variability, while aggressive decay combined with EMA achieves the lowest checkpoint variability but also weakens continued optimization. Schedule-Free substantially reduces parameter variability while preserving more late-stage progress, providing a better balance between parameter stability and continued optimization. Finally, the benefits of Schedule-Free extend beyond pretraining to ReFL and generator-side DMD, demonstrating its transferability across distinct diffusion optimization settings. Overall, our results suggest that large diffusion models need more than parameter averaging alone: effective optimization requires balancing variance reduction with continued optimization.