mlsanityData to 7 Oct 2026

Combining complex Langevin dynamics with score-based and energy-based diffusion models

arXiv 2510.01328 ↗First posted 1 Oct 2025hep-lat cond-mat.dis-nn cs.LGcited by 5

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Theories with a sign problem due to a complex action or Boltzmann weight can sometimes be numerically solved using a stochastic process in the complexified configuration space. However, the probability distribution effectively sampled by this complex Langevin process is not known a priori and notoriously hard to understand. In generative AI, diffusion models can learn distributions, or their log derivatives, from data. We explore the ability of diffusion models to learn the distributions sampled by a complex Langevin process, comparing score-based and energy-based diffusion models, and speculate about possible applications.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 17 of its 64 references that are in the map. First posted on arXiv 1 Oct 2025.

Builds on

17 of 64 references.

Closest ancestors · 12

Same direction, newest first

  1. 2025Physics-Conditioned Diffusion Models for Lattice Gauge Theory8 Feb
  2. 2024On learning higher-order cumulants in diffusion models28 Oct
  3. 2024Understanding Diffusion Models by Feynman's Path Integral17 Mar
  4. 2024On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models6 Feb
  5. 2023Generative Diffusion Models for Lattice Field Theory6 Nov
  6. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theory29 Sep
  7. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC22 Feb
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Probabilistic Models19 Jun
  12. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 5

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  4. 2019Physical Symmetries Embedded in Neural Networkscited by 40
  5. 2019On approximating nabla f with neural networkscited by 18

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 4.

5 papers.

  1. 2025Scaling flow-based approaches for topology sampling in SU(3) gauge theorycited by 6
  2. 2026A scalable flow-based approach to mitigate topological freezingcited by 1
  3. 2026Machine learning for four-dimensional SU(3) lattice gauge theoriescited by 0
  4. 2026Accurate Sampling from Diffusion Modelscited by 0
  5. 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. 2024Diffusion models learn distributions generated by complex Langevin dynamics
  2. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion
  3. 2023Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicians
  4. 2025Non-asymptotic Analysis of Diffusion Annealed Langevin Monte Carlo for Generative Modelling
  5. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  6. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
  7. 2025Diffusion Models: A Mathematical Introduction
  8. 2026Training-Free Generative Sampling via Moment-Matched Score Smoothing