Diffusion-warm sampling of the XY model enables fast thermalization at scale

• URL: http://arxiv.org/abs/2606.30773v1
• Date: Mon, 29 Jun 2026 18:06:09 GMT
• Title: Diffusion-warm sampling of the XY model enables fast thermalization at scale
• Abstract summary: We introduce a novel technique for scalable sampling of spin-system states with continuous symmetries using diffusion models.<n>We show that our technique addresses the shortfalls of the Markov chain Monte Carlo in generalization to varying system sizes.
• Score: 1.9116784879310027
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a novel technique for scalable sampling of spin-system states with continuous symmetries using diffusion models. By applying our approach to the XY model, a fundamental continuous-spin model in condensed matter physics, we show that our technique addresses the shortfalls of the Markov chain Monte Carlo (MCMC) in generalization to varying system sizes. More specifically, we show that training a temperature-conditioned diffusion model on smaller-size XY model lattices enables the generation of accurate samples in larger lattice sizes. By tracking physically important observables of the model, such as spin correlations, our experiments demonstrate that diffusion sampling followed by a few MCMC steps reduces the thermalization time by an order of magnitude relative to the standard MCMC with random initialization. Our study provides valuable insight as to how generative models can be used to study continuous-state condensed matter systems at scale.

Related papers

• Sampling the Schwinger Model with Gauge-Equivariant Diffusion [0.0]
  We present a first study of a diffusion-based approach to accelerated sampling of the $N_f = 2$ lattice Schwinger model.<n>We train a U(1)-equivariant score-based generative model to sample gauge link configurations from the marginal Schwinger model.
  arXiv  Detail & Related papers  (2026-06-25T19:00:56Z)
• Toward Scalable Normalizing Flows for the Hubbard Model [0.6503514711058446]
  Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model.<n>In this work, we investigate the steps required to extend such simulations to larger lattice sizes and lower temperatures.<n>We present the scaling behavior of normalizing flows and non-equilibrium Markov chain Monte Carlo methods for this fermionic system.
  arXiv  Detail & Related papers  (2026-01-26T08:58:08Z)
• Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densities [93.13866975467549]
  We propose Progressive Inference-Time Annealing (PITA) to learn diffusion-based samplers.<n>PITA combines two complementary techniques: Annealing of the Boltzmann distribution and Diffusion smoothing.<n>It enables equilibrium sampling of N-body particle systems, Alanine Dipeptide, and tripeptides in Cartesian coordinates.
  arXiv  Detail & Related papers  (2025-06-19T17:14:22Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces novel deep dynamical models designed to represent continuous-time sequences.<n>We train the model using maximum likelihood estimation with Markov chain Monte Carlo.<n> Experimental results on oscillating systems, videos and real-world state sequences (MuJoCo) demonstrate that our model with the learnable energy-based prior outperforms existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Deep generative modelling of canonical ensemble with differentiable thermal properties [0.9421843976231371]
  We propose a variational modelling method with differentiable temperature for canonical ensembles. Using a deep generative model, the free energy is estimated and minimized simultaneously in a continuous temperature range. The training process requires no dataset, and works with arbitrary explicit density generative models.
  arXiv  Detail & Related papers  (2024-04-29T03:41:49Z)
• Learning Energy-Based Prior Model with Diffusion-Amortized MCMC [89.95629196907082]
  Common practice of learning latent space EBMs with non-convergent short-run MCMC for prior and posterior sampling is hindering the model from further progress. We introduce a simple but effective diffusion-based amortization method for long-run MCMC sampling and develop a novel learning algorithm for the latent space EBM based on it.
  arXiv  Detail & Related papers  (2023-10-05T00:23:34Z)
• MCMC-Correction of Score-Based Diffusion Models for Model Composition [2.682859657520006]
  Diffusion models can be parameterized in terms of a score or an energy function.<n>We introduce a novel MH-like acceptance rule based on line integration of the score function.
  arXiv  Detail & Related papers  (2023-07-26T07:50:41Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• GANs and Closures: Micro-Macro Consistency in Multiscale Modeling [0.0]
  We present an approach that couples physics-based simulations and biasing methods for sampling conditional distributions with Machine Learning-based conditional generative adversarial networks. We show that this framework can improve multiscale SDE dynamical systems sampling, and even shows promise for systems of increasing complexity.
  arXiv  Detail & Related papers  (2022-08-23T03:45:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.