Discrete diffusion model improves simulation of spin systems and sampling
Discrete Diffusion Models via Evolving Variational Autoregressive Networks
Machine Learning
Summary
Models that describe complex systems often need to generate realistic examples and calculate how likely these examples are, but doing both is hard. The authors created a new method that represents probabilities exactly using special neural networks and simulates changes in systems like magnetic spins in multiple dimensions. Their method calculates important physical properties accurately and can work well with existing sampling techniques to produce diverse examples, even under difficult conditions. This approach helps better understand and simulate physical systems with complex interactions.
What this means in practice
- •For computational physicists: Simulate and analyze spin systems in two and three dimensions with accurate thermodynamic property estimation using the proposed discrete diffusion framework.
- •For statistical modelers: Enhance sample diversity and acceptance rates in Monte Carlo methods for complex discrete distributions, especially at low temperatures.
Authors
Kewen Pan, Ying Tang
Abstract
Conventional score-based diffusion models learn scores without representing normalized densities, whereas tractable normalized models support both sampling and direct likelihood evaluation. A recent tensor-network approach provides such a representation but is largely restricted to low-dimensional lattices. Here we introduce a discrete diffusion model that parameterizes normalized probability distributions using variational autoregressive networks. Explicit Markov jump operators govern the forward noising and reverse denoising dynamics, extending discrete diffusion models with normalized distributions to spin systems on higher-dimensional lattices. We apply this framework to the two- and three-dimensional Ising models across ordered, critical, and disordered regimes, accurately computing thermodynamic quantities including free energy, energy, and magnetization. We further integrate the framework with Monte Carlo sampling, using adaptive diffusion steps to maintain high acceptance rates even at low temperatures while enhancing sample diversity. These results establish a neural-network framework for the discrete diffusion model with normalized probability distributions.