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This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for…

Machine Learning · Computer Science 2026-05-08 Pierre Marion , Yu-Han Wu

Despite their success in image generation, diffusion models can memorize training data, raising serious privacy and copyright concerns. Although prior work has sought to characterize, detect, and mitigate memorization, the fundamental…

Computer Vision and Pattern Recognition · Computer Science 2025-10-01 Juyeop Kim , Songkuk Kim , Jong-Seok Lee

When do diffusion models reproduce their training data, and when are they able to generate samples beyond it? A practically relevant theoretical understanding of this interplay between memorization and generalization may significantly…

Machine Learning · Computer Science 2025-08-26 Sam Buchanan , Druv Pai , Yi Ma , Valentin De Bortoli

Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…

Machine Learning · Computer Science 2026-05-21 Tim Kaiser , Markus Kollmann

Diffusion models excel at generating high-quality, diverse samples, yet they risk memorizing training data when overfit to the training objective. We analyze the distinctions between memorization and generalization in diffusion models…

Machine Learning · Computer Science 2026-02-12 Zekai Zhang , Xiao Li , Xiang Li , Lianghe Shi , Meng Wu , Molei Tao , Qing Qu

Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they…

Machine Learning · Computer Science 2025-09-03 Alessandro Favero , Antonio Sclocchi , Matthieu Wyart

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,…

Machine Learning · Computer Science 2025-02-21 Xiangming Gu , Chao Du , Tianyu Pang , Chongxuan Li , Min Lin , Ye Wang

Diffusion models are central to modern generative modeling, and understanding how they balance memorization and generalization is critical for reliable deployment. Recent work has shown that memorization in diffusion models is shaped by…

Machine Learning · Computer Science 2026-04-28 Bingqing Jiang , Difan Zou

Diffusion-based models, such as the Stable Diffusion model, have revolutionized text-to-image synthesis with their ability to produce high-quality, high-resolution images. These advancements have prompted significant progress in image…

Cryptography and Security · Computer Science 2023-12-07 Ali Naseh , Jaechul Roh , Amir Houmansadr

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

Machine Learning · Computer Science 2024-06-11 Huijie Zhang , Jinfan Zhou , Yifu Lu , Minzhe Guo , Peng Wang , Liyue Shen , Qing Qu

Diffusion models have shown strong performance in generating high-quality tabular data, but they carry privacy risks by reproducing exact training samples. While prior work focuses on dataset-level augmentation to reduce memorization,…

Machine Learning · Computer Science 2026-05-26 Zhengyu Fang , Zhimeng Jiang , Huiyuan Chen , Xiaoge Zhang , Kaiyu Tang , Xiao Li , Jing Li

Diffusion models have emerged as a powerful framework for generative modeling. At the heart of the methodology is score matching: learning gradients of families of log-densities for noisy versions of the data distribution at different…

Machine Learning · Computer Science 2025-03-19 Ricardo Baptista , Agnimitra Dasgupta , Nikola B. Kovachki , Assad Oberai , Andrew M. Stuart

Tabular data generation has attracted significant research interest in recent years, with the tabular diffusion models greatly improving the quality of synthetic data. However, while memorization, where models inadvertently replicate exact…

Machine Learning · Computer Science 2025-11-11 Zhengyu Fang , Zhimeng Jiang , Huiyuan Chen , Xiao Li , Jing Li

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse -- a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior…

Machine Learning · Computer Science 2025-12-29 Lianghe Shi , Meng Wu , Huijie Zhang , Zekai Zhang , Molei Tao , Qing Qu

Images generated by diffusion models like Stable Diffusion are increasingly widespread. Recent works and even lawsuits have shown that these models are prone to replicating their training data, unbeknownst to the user. In this paper, we…

Machine Learning · Computer Science 2023-06-01 Gowthami Somepalli , Vasu Singla , Micah Goldblum , Jonas Geiping , Tom Goldstein

There is strong empirical evidence that the state-of-the-art diffusion modeling paradigm leads to models that memorize the training set, especially when the training set is small. Prior methods to mitigate the memorization problem often…

Machine Learning · Computer Science 2026-03-03 Kulin Shah , Alkis Kalavasis , Adam R. Klivans , Giannis Daras

Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research.…

Machine Learning · Computer Science 2026-02-23 Nick Dodson , Xinyu Gao , Qingsong Wang , Yusu Wang , Zhengchao Wan

Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

Machine Learning · Statistics 2026-02-02 Claudia Merger , Sebastian Goldt

Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…

Machine Learning · Statistics 2026-05-08 Flavio Nicoletti , Chenxiao Ma , Enrico Ventura , Luca Saglietti , Stefano Sarao Mannelli

Controlling memorization in diffusion models is critical for applications that require generated data to closely match the training distribution. Existing approaches mainly focus on data centric or model centric modifications, treating the…

Machine Learning · Computer Science 2026-01-30 Thuy Phuong Vu , Mai Viet Hoang Do , Minhhuy Le , Dinh-Cuong Hoang , Phan Xuan Tan
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