Benign Overfitting Does Not Occur in Diffusion Models

Benign overfitting and double descent have shaped our understanding of generalization in deep learning, painting a consistent picture: overfitting is not only compatible with good generalization but can actively benefit it. Since diffusion models share much of the machinery of standard deep learning, it is natural to assume that they also exhibit these properties. In this work, we show that this assumption is largely incorrect. We establish a fundamental impossibility result: for any score network architecture, overfitting and good generalization cannot occur simultaneously unless the sample size grows exponentially with the intrinsic dimension of the data. Through a linear model analysis, we trace this to a key difference between regression and score matching: regression benefits from a kernel–target alignment that is absent in score matching, making overfitting irreparably harmful. We then examine mechanisms that prevent overfitting, identifying implicit regularization from time-smoothness in the score, and early stopping in training. Our findings are then supported by high-dimensional experiments. Together, our results indicate that generalization in diffusion models is governed by mechanisms distinct from those of classical settings.