On Memorization in Diffusion Models

2023-10-04

arXiv.org

AI Summary

Diffusion models trained on small-scale datasets often exhibit counterproductive memorization—reproducing training samples rather than learning the underlying data distribution, thereby impairing generalization. Method: We introduce the Effective Model Memory (EMM) metric, the largest training set size for which a model can still approach the theoretical optimal solution. Leveraging denoising score matching theory, controlled ablation experiments, and adversarial perturbation tests (e.g., random label assignment), we systematically dissect how data distribution, model architecture, and training dynamics jointly determine the memorization boundary. Contribution/Results: Our analysis reveals that anomalous conditions—particularly random labeling—strongly trigger memorization. EMM serves as a practical, quantifiable early-warning indicator of memorization risk. All code and experimental protocols are publicly released to ensure full reproducibility.

Abstract

Due to their capacity to generate novel and high-quality samples, diffusion models have attracted significant research interest in recent years. Notably, the typical training objective of diffusion models, i.e., denoising score matching, has a closed-form optimal solution that can only generate training data replicating samples. This indicates that a memorization behavior is theoretically expected, which contradicts the common generalization ability of state-of-the-art diffusion models, and thus calls for a deeper understanding. Looking into this, we first observe that memorization behaviors tend to occur on smaller-sized datasets, which motivates our definition of effective model memorization (EMM), a metric measuring the maximum size of training data at which a learned diffusion model approximates its theoretical optimum. Then, we quantify the impact of the influential factors on these memorization behaviors in terms of EMM, focusing primarily on data distribution, model configuration, and training procedure. Besides comprehensive empirical results identifying the influential factors, we surprisingly find that conditioning training data on uninformative random labels can significantly trigger the memorization in diffusion models. Our study holds practical significance for diffusion model users and offers clues to theoretical research in deep generative models. Code is available at https://github.com/sail-sg/DiffMemorize.

Problem

• Memorization in diffusion models
• Effective model memorization metric
• Factors influencing memorization behavior

Innovation

• Defined effective model memorization
• Quantified memorization impact factors
• Utilized uninformative random labels