Diffusion Models Generalize but Not in the Way You Might Think

Abstract: Standard evaluation metrics suggest that Denoising Diffusion Models based on U-Net or Transformer architectures generalize well in practice. However, as it can be shown that an optimal Diffusion Model fully memorizes the training data, the model error determines generalization. Here, we show that although sufficiently large denoiser models show increasing memorization of the training set with increasing training time, the resulting denoising trajectories do not follow this trend. Our experiments indicate that the reason for this observation is rooted in the fact that overfitting occurs at intermediate noise levels, but the distribution of noisy training data at these noise levels has little overlap with denoising trajectories during inference. To gain more insight, we make use of a 2D toy diffusion model to show that overfitting at intermediate noise levels is largely determined by model error and the density of the data support. While the optimal denoising flow field localizes sharply around training samples, sufficient model error or dense support on the data manifold suppresses exact recall, yielding a smooth, generalizing flow field. To further support our results, we investigate how several factors, such as training time, model size, dataset size, condition granularity, and diffusion guidance, influence generalization behavior.