This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain with a target stationary distribution for an ideal denoiser trained on samples of the target distribution. This observation can be made exact for any denoiser by applying a Metropolis-Hastings step whose acceptance ratio includes the density of the forward and reverse paths of a discrete time SDE approximation. We therefore propose to train denoising diffusion models on locally convergent MALA samples to learn global MCMC proposals. We call the composition of the global denoiser-based path sampler and a local MALA sampler Denoising Diffusion Monte Carlo (DDMC). Experiments show that DDMC can provide global proposals with high acceptance across a variety of complex target densities. Our results offer preliminary evidence that the established scaling behavior of standard diffusion training transfers directly to exact sampling from high-dimensional unnormalized densities.
We develop a contraction-based framework for proving mixing-time bounds for Markov chain Monte Carlo algorithms. The framework is built around global and local contraction coefficients of Markov kernels under the $\mathsf E_γ$-divergence with $γ\ge1$. For projected Langevin Monte Carlo on a compact convex domain, we show that Gaussian smoothing yields an explicit global contraction coefficient for the $\mathsf E_γ$-divergence. This gives a direct proof of exponential convergence to the discretized stationary distribution for general smooth, possibly non-convex potentials. The rate is explicit, accommodates arbitrary random-batch sampling schemes, and yields convergence guarantees for several divergences, including KL, $χ^2$, and Rényi divergences. For independent Metropolis--Hastings with target $π$, proposal $q$, and unbounded importance weight $w=dπ/dq$, global contraction coefficients are typically trivial. We therefore introduce a local contraction coefficient on the core $C_R=\{w\le R\}$ and prove that it controls the rejection profile on the core. This yields warm-start convergence bounds governed by the local contraction coefficient and the tail profile $H_R=π(w>R)$, recovering sharp existing moment-based convergence rates when $\mathbb E_q[w^p]<\infty$ for some $p>1$, while remaining effective in heavy-tailed regimes where no finite moment of order $p>1$ exists.