From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers

2026-03-29

AI Summary

This work addresses the limitation of conventional diffusion models, which rely on independent noise injection and struggle to capture complex distributions with spatial correlations. The authors propose a novel diffusion mechanism that replaces independent sampling in both forward and reverse processes with Markov chain Monte Carlo (MCMC) dynamics informed by known interaction structures. Notably, they explicitly embed Ising couplings into the diffusion process for the first time. This approach naturally aligns with probabilistic-bit (p-bit)-based p-computer hardware architectures, thereby expanding the design space for stochastic kernels in diffusion models. Experiments on the 2D ferromagnetic Ising model and the 3D Edwards–Anderson spin glass demonstrate that the proposed method generates samples closer to the ground-truth MCMC reference distribution while achieving higher sampling throughput and energy efficiency.

Abstract

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current implementations usually place most computation in the neural network, but diffusion as a framework allows a broader range of choices for the stochastic transition kernel. Here, we generalize the stochastic sampling component by replacing independent noise injection with Markov chain Monte Carlo (MCMC) dynamics that incorporate known interaction structure. Standard independent diffusion is recovered as a special case when couplings are set to zero. By explicitly incorporating Ising couplings into the diffusion dynamics, the noising and denoising processes exploit spatial correlations representative of the target system. The resulting framework maps naturally onto probabilistic computers (p-computers) built from probabilistic bits (p-bits), which provide orders-of-magnitude advantages in sampling throughput and energy efficiency over GPUs. We demonstrate the approach on equilibrium states of the 2D ferromagnetic Ising model and the 3D Edwards-Anderson spin glass, showing that correlated diffusion produces samples in closer agreement with MCMC reference distributions than independent diffusion. More broadly, the framework shows that p-computers can enable new classes of diffusion algorithms that exploit structured probabilistic sampling for generative modeling.

Problem

• diffusion models
• correlated sampling
• spatial correlations
• generative modeling
• probabilistic computers

Innovation

• correlated diffusion
• probabilistic computers
• Ising couplings
• structured sampling
• generative modeling