Diffusion models defy deep learning trends: overfitting is always harmful

A new paper by Farghly, Dupuis, Durmus, and Simsekli (arXiv:2607.02671, 2026) delivers a counterintuitive result: the well-known phenomenon of benign overfitting—where models generalize well despite fitting noise—does not occur in diffusion models. The authors prove fundamental impossibility theorems showing that overfitting and good generalization cannot coexist in these models unless the training sample size grows exponentially with the data dimension. In practice, this means that as image resolution or data complexity increases, the number of training examples needed to avoid performance collapse becomes astronomically large. The population loss exhibits a classical U-shaped curve as model complexity increases, rather than the double-descent pattern seen in neural networks for regression tasks.

The key mechanistic difference lies in the objective: regression benefits from alignment between the target signal and the empirical covariance of the data, but score matching—the objective used to train diffusion models—admits no such alignment. This leaves overfitting irreparably harmful. The paper also identifies two implicit regularization mechanisms that help practitioners avoid the worst pitfalls: the temporal smoothness of the score function across diffusion time steps, and early stopping during training. High-dimensional image generation experiments confirm the theoretical findings, showing that overparameterized diffusion models degrade rapidly if trained too long. For AI engineers and researchers, this work underscores that diffusion models have fundamentally different generalization behavior than classifiers, and that strategies like early stopping and careful capacity control are essential for robust generative performance.