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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

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

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

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

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we…

Machine Learning · Computer Science 2025-10-29 Tony Bonnaire , Raphaël Urfin , Giulio Biroli , Marc Mézard

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

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 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

Multimodal machine learning, especially text-to-image models like Stable Diffusion and DALL-E 3, has gained significance for transforming text into detailed images. Despite their growing use and remarkable generative capabilities, there is…

Computer Vision and Pattern Recognition · Computer Science 2023-12-14 Ali Naseh , Jaechul Roh , Amir Houmansadr

Generative neural networks learn how to produce highly realistic images from a large, but finite number of examples - or do they simply memorise their training set? To settle this question, Kadkhodaie, Guth, Simoncelli and Mallat (ICLR '24)…

Machine Learning · Statistics 2026-05-21 Antoine Maillard , Sebastian Goldt

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

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

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

Large-scale text-to-image diffusion models excel in generating high-quality images from textual inputs, yet concerns arise as research indicates their tendency to memorize and replicate training data, raising We also addressed the issue of…

Computer Vision and Pattern Recognition · Computer Science 2024-06-28 Ruchika Chavhan , Ondrej Bohdal , Yongshuo Zong , Da Li , Timothy Hospedales

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

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

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

Autoregressive language models (ARMs) have been shown to memorize and occasionally reproduce training data verbatim, raising concerns about privacy and copyright liability. Diffusion language models (DLMs) have recently emerged as a…

Computation and Language · Computer Science 2026-03-04 Xiaoyu Luo , Wenrui Yu , Qiongxiu Li , Johannes Bjerva

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence…

Machine Learning · Statistics 2021-03-03 Hongkang Yang , Weinan E

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

Machine Learning · Computer Science 2025-03-13 Puheng Li , Zhong Li , Huishuai Zhang , Jiang Bian
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