mlsanityData to 14 Oct 2026

In search of dispersed memories: Generative diffusion models are associative memory networks

arXiv 2309.17290 ↗First posted 29 Sep 2023stat.ML cs.LGcited by 44

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Uncovering the mechanisms behind long-term memory is one of the most fascinating open problems in neuroscience and artificial intelligence. Artificial associative memory networks have been used to formalize important aspects of biological memory. Generative diffusion models are a type of generative machine learning techniques that have shown great performance in many tasks. Like associative memory systems, these networks define a dynamical system that converges to a set of target states. In this work we show that generative diffusion models can be interpreted as energy-based models and that, when trained on discrete patterns, their energy function is (asymptotically) identical to that of modern Hopfield networks. This equivalence allows us to interpret the supervised training of diffusion models as a synaptic learning process that encodes the associative dynamics of a modern Hopfield network in the weight structure of a deep neural network. Leveraging this connection, we formulate a generalized framework for understanding the formation of long-term memory, where creative generation and memory recall can be seen as parts of a unified continuum.

Key facts. Cited by 44 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 14 of its 59 references that are in the map. First posted on arXiv 29 Sep 2023.

Builds on

14 of 59 references.

Closest ancestors · 4

Same direction, newest first

  1. 2023Spontaneous Symmetry Breaking in Generative Diffusion Models31 May
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  3. 2020Denoising Diffusion Implicit Models6 Oct
  4. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 10

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2017Gradient Episodic Memory for Continual Learningcited by 1,898
  3. 2020Hopfield Networks is All You Needcited by 475
  4. 2016Dense Associative Memory for Pattern Recognitioncited by 236
  5. 2018Meta-Reinforcement Learning of Structured Exploration Strategiescited by 130
  6. 2020Large Associative Memory Problem in Neurobiology and Machine Learningcited by 112
  7. 2014Deep Neural Networks Reveal a Gradient in the Complexity of Neural Representations across the Brain's Ventral Visual Pathwaycited by 94
  8. 2021Predictive Coding: a Theoretical and Experimental Reviewcited by 77
  9. 2020The Neural Coding Framework for Learning Generative Modelscited by 44
  10. 2021Associative Memories via Predictive Codingcited by 44

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 13; 2025: 11; 2026: 18.

44 papers.

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  1. 2024An analytic theory of creativity in convolutional diffusion modelscited by 104
  2. 2024On Statistical Rates and Provably Efficient Criteria of Latent Diffusion Transformers (DiTs)cited by 40
  3. 2023The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instabilitycited by 39
  4. 2024Losing dimensions: Geometric memorization in generative diffusioncited by 29
  5. 2024Dynamic Negative Guidance of Diffusion Modelscited by 28
  6. 2024Classifier-Free Guidance inside the Attraction Basin May Cause Memorizationcited by 21
  7. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curvescited by 20
  8. 2025Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modelingcited by 18
  9. 2025The Information Dynamics of Generative Diffusioncited by 13
  10. 2025Generalization of Diffusion Models Arises with a Balanced Representation Spacecited by 11
  11. 2025Generalization Dynamics of Linear Diffusion Modelscited by 9
  12. 2024Random Features Hopfield Networks generalize retrieval to previously unseen examplescited by 8
32 more
  1. 2024Dense Associative Memory Through the Lens of Random Featurescited by 8
  2. 2025In-context denoising with one-layer transformers: connections between attention and associative memory retrievalcited by 7
  3. 2024Heuristically Adaptive Diffusion-Model Evolutionary Strategycited by 6
  4. 2026A Random Matrix Theory Perspective on the Consistency of Diffusion Modelscited by 6
  5. 2024Bridging Associative Memory and Probabilistic Modelingcited by 5
  6. 2024Hierarchical Associative Memory, Parallelized MLP-Mixer, and Symmetry Breakingcited by 5
  7. 2026Local Coverage Governs Memorization in Diffusion Modelscited by 5
  8. 2023Inverse distance weighting attentioncited by 4
  9. 2024Dense Hopfield Networks in the Teacher-Student Settingcited by 4
  10. 2024Explosive neural networks via higher-order interactions in curved statistical manifoldscited by 3
  11. 2024Self-attention as an attractor network: transient memories without backpropagationcited by 3
  12. 2026Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balancecited by 3
  13. 2026Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Datacited by 3
  14. 2025Understanding Generalization in Diffusion Distillation via Probability Flow Distancecited by 2
  15. 2025Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplingscited by 2
  16. 2026Deep Clustering with Associative Memoriescited by 2
  17. 2025Neural Learning Rules from Associative Networks Theorycited by 1
  18. 2026Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systemscited by 1
  19. 2026Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamicscited by 1
  20. 2026The two clocks and the innovation window: When and how generative models learn rulescited by 1
  21. 2026Self-Regulating Annealing in Heavy-Tailed Diffusion Modelscited by 1
  22. 2026Evaluating the Representation Space of Diffusion Models via Self-Supervised Principlescited by 1
  23. 2025Binding threshold units with artificial oscillatory neuronscited by 0
  24. 2025What Neuroscience Can Teach AI About Learning in Continuously Changing Environmentscited by 0
  25. 2026Coupled Inference in Diffusion Models for Semantic Decompositioncited by 0
  26. 2026Geometry-Aware Attention Guidance for Diffusion Models via Modern Hopfield Dynamicscited by 0
  27. 2026On associative neural networks for sparse patterns with huge capacitiescited by 0
  28. 2026Language Diffusion Models are Associative Memories Capable of Retrieving Unseen Datacited by 0
  29. 2026Fault tolerance estimation in digital circuits with visualised generative networkscited by 0
  30. 2026Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspectivecited by 0
  31. 2026Continual Learning in Modern Hopfield Networks with an Application to Diffusion Modelscited by 0
  32. 2026Retrieval-Warmed Energy-Based Reasoning: A Five-Arm Ablation Methodology for Diffusion-as-Inference on Structured Reasoning Taskscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Memorization to Generalization: Emergence of Diffusion Models from Associative Memory
  2. 2023Memory in Plain Sight: Surveying the Uncanny Resemblances of Associative Memories and Diffusion Models
  3. 2025Modern Methods in Associative Memory
  4. 2025Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training
  5. 2026Hierarchical Prototype Emergence in Modern Hopfield Models
  6. 2026Memorisation, convergence and generalisation in generative models
  7. 2024Spiking Diffusion Models
  8. 2024Demolition and Reinforcement of Memories in Spin-Glass-like Neural Networks