相关论文: Metropolis-Adjusted Diffusion Models

The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…

Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…

In this paper, we study the problem of sampling from a given probability density function that is known to be smooth and strongly log-concave. We analyze several methods of approximate sampling based on discretizations of the (highly…

This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed…

Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth…

Langevin Dynamics has been extensively employed in global non-convex optimization due to the concentration of its stationary distribution around the global minimum of the potential function at low temperatures. In this paper, we propose to…

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…

Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

We give lower bounds on the performance of two of the most popular sampling methods in practice, the Metropolis-adjusted Langevin algorithm (MALA) and multi-step Hamiltonian Monte Carlo (HMC) with a leapfrog integrator, when applied to…

We prove that a denoising diffusion sampler equipped with a sequential bias across the batch dimension is exactly an Euler-Maruyama integrator for overdamped Langevin dynamics. Each reverse denoising step, with its associated spring…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However,…

The diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each…

To sample from a general target distribution $p_*\propto e^{-f_*}$ beyond the isoperimetric condition, Huang et al. (2023) proposed to perform sampling through reverse diffusion, giving rise to Diffusion-based Monte Carlo (DMC).…

Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…

In this paper, we propose irreversible versions of the Metropolis Hastings (MH) and Metropolis adjusted Langevin algorithm (MALA) with a main focus on the latter. For the former, we show how one can simply switch between different proposal…

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…