Why diffusion models do not memorize: the role of implicit dynamical regularization in training
Diffusion models have attained remarkable success across a wide range of generative tasks. A key challenge lies in understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time τgen at which models begin to generate high-quality samples and a later time τmem beyond which memorization emerges. Crucially, we found that τmem increases linearly with the training set size n, whereas τgen remains constant. This creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when n becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allows to avoid memorization even in highly overparameterized settings. Our findings are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, alongside a theoretical analysis using a tractable random features model studied in the high-dimensional limit.44 https://github.com/tbonnair/Why-Diffusion-Models-Don-t-Memorize. https://github.com/tbonnair/Why-Diffusion-Models-Don-t-Memorize.