Problem
Research questions and friction points this paper is trying to address.
Discrete Diffusion Models
Normalized Probability Distributions
Higher-dimensional Lattices
Thermodynamic Quantities
Discrete Diffusion Models via Evolving Variational Autoregressive Networks
🤖 AI Summary
本文通过使用变分自回归网络参数化归一化概率分布，解决了在高维晶格上离散扩散模型的应用问题，并结合蒙特卡洛采样提高了接受率和样本多样性。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
variational autoregressive networks
normalized probability distributions
Markov jump operators
high-dimensional lattices
adaptive diffusion steps
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