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We study the memorization and generalization capabilities of Diffusion Models (DMs) when data lies on a structured latent manifold. Specifically, we consider a set of $P$ data points in $N$ dimensions confined to a latent subspace of…

Disordered Systems and Neural Networks · Physics 2025-05-27 Beatrice Achilli , Luca Ambrogioni , Carlo Lucibello , Marc Mézard , Enrico Ventura

Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with analytic transition kernels and score functions. The…

Machine Learning · Statistics 2024-03-01 Guan-Horng Liu , Tianrong Chen , Evangelos A. Theodorou , Molei Tao

Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…

Disordered Systems and Neural Networks · Physics 2026-03-24 David G. Clark

Diffusion models have emerged as a popular family of deep generative models (DGMs). In the literature, it has been claimed that one class of diffusion models -- denoising diffusion probabilistic models (DDPMs) -- demonstrate superior image…

Image and Video Processing · Electrical Eng. & Systems 2023-09-20 Rucha Deshpande , Muzaffer Özbey , Hua Li , Mark A. Anastasio , Frank J. Brooks

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

It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…

Artificial Intelligence · Computer Science 2007-05-23 Petro M. Gopych

Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…

Disordered Systems and Neural Networks · Physics 2024-02-14 Carlo Lucibello , Marc Mézard

Recent endeavors in Multimodal Large Language Models (MLLMs) aim to unify visual comprehension and generation by combining LLM and diffusion models, the state-of-the-art in each task, respectively. Existing approaches rely on spatial visual…

Computer Vision and Pattern Recognition · Computer Science 2025-04-22 Kaihang Pan , Wang Lin , Zhongqi Yue , Tenglong Ao , Liyu Jia , Wei Zhao , Juncheng Li , Siliang Tang , Hanwang Zhang

Diffusion models (DMs) have demonstrated exceptional generative capabilities across various domains, including image, video, and so on. A key factor contributing to their effectiveness is the high quantity and quality of data used during…

Computer Vision and Pattern Recognition · Computer Science 2025-03-03 Qianlong Xiang , Miao Zhang , Yuzhang Shang , Jianlong Wu , Yan Yan , Liqiang Nie

Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at…

Machine Learning · Computer Science 2016-05-31 Chongxuan Li , Jun Zhu , Bo Zhang

Pretrained diffusion models and their outputs are widely accessible due to their exceptional capacity for synthesizing high-quality images and their open-source nature. The users, however, may face litigation risks owing to the models'…

Computer Vision and Pattern Recognition · Computer Science 2024-04-02 Chen Chen , Daochang Liu , Chang Xu

Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2023-08-23 Xingyi Yang , Xinchao Wang

Text-to-image diffusion models (DMs) have achieved remarkable success in image generation. However, concerns about data privacy and intellectual property remain due to their potential to inadvertently memorize and replicate training data.…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Antoni Kowalczuk , Dominik Hintersdorf , Lukas Struppek , Kristian Kersting , Adam Dziedzic , Franziska Boenisch

Evidence accumulation models (EAMs) provide a powerful framework for inferring latent cognitive processes from choice and reaction time data. While EAMs are traditionally limited to binary choices, recent developments have extended them to…

Methodology · Statistics 2026-05-12 Yufei Wu , Tamás Szűcs , Agnes Moors , Francis Tuerlinckx

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Machine Learning · Computer Science 2024-11-01 Guande He , Kaiwen Zheng , Jianfei Chen , Fan Bao , Jun Zhu

The entropic associative memory (EAM) is a computational model of natural memory incorporating some of its putative properties of being associative, distributed, declarative, abstractive and constructive. Previous experiments satisfactorily…

Machine Learning · Computer Science 2024-05-22 Noé Hernández , Rafael Morales , Luis A. Pineda

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises…

Computation and Language · Computer Science 2025-05-27 Litu Rout , Constantine Caramanis , Sanjay Shakkottai

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion…

Computation and Language · Computer Science 2026-05-11 Georgios Batzolis , Mark Girolami , Luca Ambrogioni

The ability of machine learning models to store input information in hidden layer vector embeddings, analogous to the concept of `memory', is widely employed but not well characterized. We find that language model embeddings typically…

Computation and Language · Computer Science 2026-05-20 Benjamin L. Badger

World models represent a promising approach for training reinforcement learning agents with significantly improved sample efficiency. While most world model methods primarily rely on sequences of discrete latent variables to model…

Machine Learning · Computer Science 2025-06-17 Jia-Hua Lee , Bor-Jiun Lin , Wei-Fang Sun , Chun-Yi Lee