Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler

arXiv:2609.28338 · math.PR, cs.LG, stat.CO, stat.ML · Submitted 2026-09-23 · Read on arXiv

math.PR, cs.LG, stat.CO, stat.ML

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Accuracy — 25× in this paper · explained in 1 episode
• Spectral Gap — 21× in this paper · explained in 5 episodes
• Diffusion Model — 5× in this paper · explained in 8 episodes
• Diffusion Models — 4× in this paper · explained in 6 episodes
• Metastability — 4× in this paper · explained in 3 episodes
• Score Function — 4× in this paper · explained in 4 episodes
• Wasserstein Distance — 4× in this paper · explained in 4 episodes
• Diffusion Processes — 2× in this paper · explained in 2 episodes
• Fisher Information — 2× in this paper · explained in 3 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Metropolis-adjusted Langevin Algorithm — 2× in this paper
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Ornstein–Uhlenbeck Process — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Mirror Langevin diffusions: Convergence rates and Markov chain approximations
• High-accuracy sampling for diffusion models and log-concave distributions
• Markov Chain Monte Carlo with Diffusion Paths
• Exact Global MCMC with Denoising Diffusion
• A Proximal Algorithm for Sampling
• Alternating Diffusion for Proximal Sampling with Zeroth Order Queries

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