mlsanityData to 7 Oct 2026

Generative Diffusion Models for Lattice Field Theory

arXiv 2311.03578 ↗First posted 6 Nov 2023hep-lat cs.LGcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

This study delves into the connection between machine learning and lattice field theory by linking generative diffusion models (DMs) with stochastic quantization, from a stochastic differential equation perspective. We show that DMs can be conceptualized by reversing a stochastic process driven by the Langevin equation, which then produces samples from an initial distribution to approximate the target distribution. In a toy model, we highlight the capability of DMs to learn effective actions. Furthermore, we demonstrate its feasibility to act as a global sampler for generating configurations in the two-dimensional φ4 quantum lattice field theory.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 13 of its 29 references that are in the map. First posted on arXiv 6 Nov 2023.

Builds on

13 of 29 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theory29 Sep
  2. 2023Renormalizing Diffusion Models23 Aug
  3. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep

Other references · 10

  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  2. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 147
  3. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  4. 2022Score-based Generative Models for Calorimeter Shower Simulationcited by 52
  5. 2022Learning Lattice Quantum Field Theories with Equivariant Continuous Flowscited by 37
  6. 2022Aspects of scaling and scalability for flow-based sampling of lattice QCDcited by 26
  7. 2021Flow-based sampling for multimodal and extended-mode distributions in lattice field theorycited by 25
  8. 2023Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theoriescited by 25
  9. 2021Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flowscited by 24
  10. 2023Advances in machine-learning-based sampling motivated by lattice quantum chromodynamicscited by 23

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 6; 2025: 3; 2026: 3.

13 papers.

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  1. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  2. 2024Target Score Matchingcited by 46
  3. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  4. 2024On learning higher-order cumulants in diffusion modelscited by 10
  5. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theorycited by 9
  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. 2024Diffusion models learn distributions generated by complex Langevin dynamicscited by 2
  11. 2026Capturing the Topological Phase Transition and Thermodynamics of the 2D XY Model via Manifold-Aware Score-Based Generative Modelingcited by 0
  12. 2026Symbolic Density Estimators for Unnormalized Distributionscited by 0
1 more
  1. 2026Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discoverycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Quantum-Noise-Driven Generative Diffusion Models
  2. 2026Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory
  3. 2026From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers
  4. 2024Understanding Diffusion Models by Feynman's Path Integral
  5. 2024Discrete generative diffusion models without stochastic differential equations: a tensor network approach
  6. 2024New algorithms for sampling and diffusion models
  7. 2024Nonequilbrium physics of generative diffusion models
  8. 2025Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion