Reproduce “Exact Global MCMC with Denoising Diffusion” on OpenResearch

About this paper

Mitch Hill

The Denoising Diffusion Monte Carlo (DDMC) algorithm introduces an exact MCMC sampler leveraging standard denoising diffusion models to generate global proposals for complex, high-dimensional target distributions. It demonstrated successful mode weight repair on Gaussian mixtures and achieved competitive energy distances for Lennard-Jones clusters and faster cold-start convergence for a 550D BNN posterior.

Key insights

• Applying a Metropolis-Hastings correction to the full discrete diffusion path ensures the exactness of the MCMC chain, effectively absorbing any biases or imperfections arising from the learned denoiser or the training data distribution.
• Standard denoising diffusion models, proven effective in generative tasks, can be successfully adapted for exact MCMC sampling when integrated with path-space MH, leveraging their scalability and robustness without relying on complex, on-policy variational objectives.
• Composing global diffusion-based proposals with local MALA steps creates a robust and efficient sampler that benefits from both wide exploration across modes and fine-grained local refinement, degrading gracefully to MALA if global proposals are rejected.

Summary by alphaXiv.