Why diffusion models do not memorize: the role of implicit dynamical regularization in training
Abstract
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 τ gen at which models begin to generate high-quality samples and a later time τ mem beyond which memorization emerges. Crucially, we found that τ mem increases linearly with the training set size n, whereas τ gen 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 3 Equal contribution.
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BibTeX
@article{bonnaire2026diffusion,
title = {{Why diffusion models do not memorize: the role of implicit dynamical regularization in training}},
author = {Tony Bonnaire and Raphaël Urfin and Giulio Biroli and Marc Mezard},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
year = {2026},
month = aug,
doi = {10.1088/1742-5468/ae7e6a},
url = {https://hal.science/hal-05767724v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Why diffusion models do not memorize: the role of implicit dynamical regularization in training
AU - Tony Bonnaire
AU - Raphaël Urfin
AU - Giulio Biroli
AU - Marc Mezard
PY - 2026
DA - 2026/08/19
JO - Journal of Statistical Mechanics: Theory and Experiment
DO - 10.1088/1742-5468/ae7e6a
UR - https://hal.science/hal-05767724v1
AB - 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 τ gen at which models begin to generate high-quality samples and a later time τ mem beyond which memorization emerges. Crucially, we found that τ mem increases linearly with the training set size n, whereas τ gen 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 3 Equal contribution.
SN - 1742-5468
ER -