mlsanityData to 14 Oct 2026

Diffusion Models as Stochastic Quantization in Lattice Field Theory

arXiv 2309.17082 ↗First posted 29 Sep 2023hep-lat cs.LGcited by 24

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional φ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 27 of its 85 references that are in the map. First posted on arXiv 29 Sep 2023.

Builds on

27 of 85 references.

Closest ancestors · 5

Same direction, newest first

  1. 2023Renormalizing Diffusion Models23 Aug
  2. 2022Diffusion Models in Vision: A Survey10 Sep
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 22

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  3. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  6. 2020Equivariant flow-based sampling for lattice gauge theorycited by 103
  7. 2022AUC Maximization in the Era of Big Data and AI: A Surveycited by 100
  8. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 88
  9. 2022Score-based Generative Models for Calorimeter Shower Simulationcited by 52
  10. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  11. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  12. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
10 more
  1. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 31
  2. 2021Flow-based sampling for fermionic lattice field theoriescited by 27
  3. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  4. 2021Flow-based sampling for multimodal and extended-mode distributions in lattice field theorycited by 25
  5. 2022Stochastic normalizing flows as non-equilibrium transformationscited by 25
  6. 2023Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theoriescited by 25
  7. 2022Flow-based sampling in the lattice Schwinger model at criticalitycited by 20
  8. 2021Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Modelscited by 18
  9. 2022Applications of Machine Learning to Lattice Quantum Field Theorycited by 14
  10. 2023Geometrical aspects of lattice gauge equivariant convolutional neural networkscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 6; 2025: 6; 2026: 10.

24 papers.

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  1. 2023Generative Diffusion Models for Lattice Field Theorycited by 13
  2. 2024Understanding Diffusion Models by Feynman's Path Integralcited by 13
  3. 2024On learning higher-order cumulants in diffusion modelscited by 10
  4. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  5. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  6. 2025Combining complex Langevin dynamics with score-based and energy-based diffusion modelscited by 5
  7. 2024Neural network representation of quantum systemscited by 4
  8. 2023Fixed point actions from convolutional neural networkscited by 3
  9. 2025Group-Equivariant Diffusion Models for Lattice Field Theorycited by 3
  10. 2024Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural networkcited by 2
  11. 2024Diffusion models learn distributions generated by complex Langevin dynamicscited by 2
  12. 2025The neural networks with tensor weights and emergent fermionic Wick rules in the large-width limitcited by 2
12 more
  1. 2026Generative Models and Statistical Validationcited by 2
  2. 2025NeuMC -- a package for neural sampling for lattice field theoriescited by 1
  3. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  4. 2026The critical slowing down in training diffusion modelscited by 1
  5. 2024Flow Perturbation to Accelerate Unbiased Sampling of Boltzmann distributioncited by 0
  6. 2026Flow Perturbation++: Multi-Step Unbiased Jacobian Estimation for High-Dimensional Boltzmann Samplingcited by 0
  7. 2026Machine learning for four-dimensional SU(3) lattice gauge theoriescited by 0
  8. 2026Sampling the Schwinger Model with Gauge-Equivariant Diffusioncited by 0
  9. 2026Renormalization Group Flow Matching for Scalable Local Generative Modelingcited by 0
  10. 2026FUND: Density Flow for Sampling Unnormalised Distributionscited by 0
  11. 2026Generative Modeling of Stochastic Dynamics for Long-Time Evolutioncited by 0
  12. 2026Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discoverycited by 0

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  2. 2026Data Free Training of Diffusion Models for Lattice Field Theories
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  4. 2026From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers
  5. 2026Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory
  6. 2026An Hybrid Quantum-Classical Diffusion Model for Image Generation
  7. 2025Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning
  8. 2025Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion