From Independent to Correlated Diffusion: Generalized Generative Modeling with Probabilistic Computers
This work introduces a new paradigm for generative modeling that leverages structured probabilistic sampling, enabling efficient implementation on probabilistic computers for domain-specific problems like statistical physics.
The authors generalize diffusion models by replacing independent noise injection with MCMC dynamics that incorporate known interaction structure, enabling correlated diffusion. They demonstrate on 2D Ising and 3D spin glass models that correlated diffusion produces samples closer to MCMC reference distributions than independent diffusion, and map the framework onto probabilistic computers for orders-of-magnitude sampling throughput and energy efficiency gains over GPUs.
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.