相关论文: Metropolis-Adjusted Diffusion Models

For sufficiently smooth targets of product form it is known that the variance of a single coordinate of the proposal in RWM (Random walk Metropolis) and MALA (Metropolis adjusted Langevin algorithm) should optimally scale as $n^{-1}$ and as…

The preconditioned Metropolis adjusted Langevin algorithm (MALA) is a widely used method in statistical applications, where the choice of the preconditioning matrix plays a critical role. Recently, Titsias \cite{Titsias2024} demonstrated…

Diffusion magnetic resonance imaging datasets suffer from low Signal-to-Noise Ratio, especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and…

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

In this article, we study the problem of sampling from distributions whose densities are not necessarily smooth nor logconcave. We propose a simple Langevin-based algorithm that does not rely on popular but computationally challenging…

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a…

Understanding the complexity of sampling from a strongly log-concave and log-smooth distribution $\pi$ on $\mathbb{R}^d$ to high accuracy is a fundamental problem, both from a practical and theoretical standpoint. In practice, high-accuracy…

This paper considers the optimal scaling problem for high-dimensional random walk Metropolis algorithms for densities which are differentiable in Lp mean but which may be irregular at some points (like the Laplace density for example)…

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…

We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the L^2 errors (more generally L^p errors) in the estimate of the…

Over the past few years, several approaches utilizing score-based diffusion have been proposed to sample from probability distributions, that is without having access to exact samples and relying solely on evaluations of unnormalized…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

We develop a class of interacting particle systems for implementing a maximum marginal likelihood estimation (MMLE) procedure to estimate the parameters of a latent variable model. We achieve this by formulating a continuous-time…

We consider the problem of sampling distributions stemming from non-convex potentials with Unadjusted Langevin Algorithm (ULA). We prove the stability of the discrete-time ULA to drift approximations under the assumption that the potential…

Efficient text-to-image generation remains a challenging task due to the high computational costs associated with the multi-step sampling in diffusion models. Although distillation of pre-trained diffusion models has been successful in…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform…

The usage of positive definite metric tensors derived from second derivative information in the context of the simplified manifold Metropolis adjusted Langevin algorithm (MALA) is explored. A new adaptive step length procedure that resolves…

We study sampling from posterior distributions with nonsmooth composite potentials, a setting in which proximal-based Langevin methods are theoretically appealing but in practice limited to simple functions with closed-form proximal…