mlsanityData to 7 Oct 2026

Spontaneous Symmetry Breaking in Generative Diffusion Models

arXiv 2305.19693 ↗First posted 31 May 2023cs.LG cs.CVcited by 74

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative dynamics into two distinct phases: 1) A linear steady-state dynamics around a central fixed-point and 2) an attractor dynamics directed towards the data manifold. These two "phases" are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3x FID improvements on fast samplers, while also increasing sample diversity (e.g., racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

Key facts. Cited by 74 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 27 of its 48 references that are in the map. First posted on arXiv 31 May 2023.

Builds on

27 of 48 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022An optimal control perspective on diffusion-based generative modeling2 Nov
  2. 2022Pseudo Numerical Methods for Diffusion Models on Manifolds20 Feb
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 22

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2016Improved Techniques for Training GANscited by 2,938
  3. 2022Video Diffusion Modelscited by 2,280
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  7. 2016Group Equivariant Convolutional Networkscited by 1,154
  8. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  9. 2021E(n) Equivariant Graph Neural Networkscited by 951
  10. 2016Pixel Recurrent Neural Networkscited by 814
  11. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  12. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
10 more
  1. 2023AudioLDM: Text-to-Audio Generation with Latent Diffusion Modelscited by 592
  2. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  3. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
  4. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 248
  5. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  6. 2020Normalizing Flows on Tori and Spherescited by 117
  7. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  8. 2020Sampling using SU(N) gauge equivariant flowscited by 83
  9. 2021Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifoldscited by 72
  10. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 14; 2025: 23; 2026: 31.

74 papers.

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  1. 2024MACE: Mass Concept Erasure in Diffusion Modelscited by 298
  2. 2024Dynamical Regimes of Diffusion Modelscited by 133
  3. 2024A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Datacited by 88
  4. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  5. 2023In search of dispersed memories: Generative diffusion models are associative memory networkscited by 44
  6. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 41
  7. 2023The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instabilitycited by 37
  8. 2024Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusioncited by 31
  9. 2024Losing dimensions: Geometric memorization in generative diffusioncited by 28
  10. 2024Dynamic Negative Guidance of Diffusion Modelscited by 28
  11. 2025On the Edge of Memorization in Diffusion Modelscited by 22
  12. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curvescited by 20
38 more
  1. 2025Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptivecited by 20
  2. 2025Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modelingcited by 18
  3. 2025Learning normalized image densities via dual score matchingcited by 17
  4. 2025Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorizationcited by 16
  5. 2025Feedback Guidance of Diffusion Modelscited by 16
  6. 2024Diffusion Models are Evolutionary Algorithmscited by 15
  7. 2024Detecting Out-Of-Distribution Earth Observation Images with Diffusion Modelscited by 14
  8. 2025CoDe: Blockwise Control for Denoising Diffusion Modelscited by 14
  9. 2025TRCE: Towards Reliable Malicious Concept Erasure in Text-to-Image Diffusion Modelscited by 14
  10. 2025Entropic Time Schedulers for Generative Diffusion Modelscited by 13
  11. 2023Memory in Plain Sight: Surveying the Uncanny Resemblances of Associative Memories and Diffusion Modelscited by 12
  12. 2024Cascade of phase transitions in the training of Energy-based modelscited by 12
  13. 2025The Information Dynamics of Generative Diffusioncited by 12
  14. 2025Analysis of Diffusion Models for Manifold Datacited by 11
  15. 2023How do Minimum-Norm Shallow Denoisers Look in Function Space?cited by 9
  16. 2025Neural cellular automata: applications to biology and beyond classical AIcited by 9
  17. 2023U-Turn Diffusioncited by 8
  18. 2025Local Diffusion Models and Phases of Data Distributionscited by 8
  19. 2025CE-SDWV: Effective and Efficient Concept Erasure for Text-to-Image Diffusion Models via a Semantic-Driven Word Vocabularycited by 7
  20. 2026Theory of Speciation Transitions in Diffusion Models with General Class Structurecited by 7
  21. 2026The Entropic Signature of Class Speciation in Diffusion Modelscited by 7
  22. 2025Optimizing Noise Schedules of Generative Models in High Dimensionsscited by 6
  23. 2025When Diffusion Models Memorize: Inductive Biases in Probability Flow of Minimum-Norm Shallow Neural Netscited by 6
  24. 2024Nonequilbrium physics of generative diffusion modelscited by 5
  25. 2025Measuring Semantic Information Production in Generative Diffusion Modelscited by 5
  26. 2026Layer-wise Instance Binding for Regional and Occlusion Control in Text-to-Image Diffusion Transformerscited by 5
  27. 2026How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Modelscited by 5
  28. 2024Latent Abstractions in Generative Diffusion Modelscited by 4
  29. 2026Dynamical Regimes of Multimodal Diffusion Modelscited by 4
  30. 2026Noise Scheduling as Information-Guided Allocation in Diffusion Trainingcited by 4
  31. 2024Self-attention as an attractor network: transient memories without backpropagationcited by 3
  32. 2025Geometric Regularity in Deterministic Sampling Dynamics of Diffusion-based Generative Modelscited by 3
  33. 2026Emergence of Distortions in High-Dimensional Guided Diffusion Modelscited by 3
  34. 2026Steering Dynamical Regimes of Diffusion Models by Breaking Detailed Balancecited by 3
  35. 2026Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Datacited by 3
  36. 2024SOWing Information: Cultivating Contextual Coherence with MLLMs in Image Generationcited by 2
  37. 2025Not Every Time and Frequency Need to Be Forgotten in Diffusion Unlearningcited by 2
  38. 2026Diffusion models recover accurate mixture weights despite score function insensitivitycited by 2

50 most cited of 74 All 74 (JSON)

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  1. 2024Input-Adaptive Generative Dynamics in Diffusion Models
  2. 2024GUD: Generation with Unified Diffusion
  3. 2026The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics
  4. 2023Infinite-Dimensional Diffusion Models
  5. 2024Tracing the Roots: Leveraging Temporal Dynamics in Diffusion Trajectories for Origin Attribution
  6. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models
  7. 2024Non-Normal Diffusion Models
  8. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models