Related papers: Diffusion at Absolute Zero: Langevin Sampling usin…

Exact-sparsity inducing prior distributions in Bayesian analysis typically lead to posterior distributions that are very challenging to handle by standard Markov Chain Monte Carlo (MCMC) methods, particular in high-dimensional models with…

Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…

In this paper, we propose a general methodology for sampling from un-normalized densities defined on Riemannian manifolds, with a particular focus on multi-modal targets that remain challenging for existing sampling methods. Inspired by the…

Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…

Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and…

Many methods that build powerful variational distributions based on unadjusted Langevin transitions exist. Most of these were developed using a wide range of different approaches and techniques. Unfortunately, the lack of a unified analysis…

The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…

Diffusion models are a remarkably effective way of learning and sampling from a distribution $p(x)$. In posterior sampling, one is also given a measurement model $p(y \mid x)$ and a measurement $y$, and would like to sample from $p(x \mid…

Let U be a given function defined on R^d and \pi(x) be a density function proportional to \exp -U(x). The following diffusion X(t) is often used to sample from \pi(x), dX(t)=-\nabla U(X(t)) dt+\sqrt2 dW(t),\qquad X(0)=x_0. To accelerate the…

We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…

In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…

Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…

Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…

In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…

Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…

This paper proposes and compares two new sampling schemes for sparse deconvolution using a Bernoulli-Gaussian model. To tackle such a deconvolution problem in a blind and unsupervised context, the Markov Chain Monte Carlo (MCMC) framework…

Sequential Monte Carlo (SMC) methods have recently shown successful results for conditional sampling of generative diffusion models. In this paper we propose a new diffusion posterior SMC sampler achieving improved statistical efficiencies,…

We study sampling problems associated with non-convex potentials that meanwhile lack smoothness. In particular, we consider target distributions that satisfy either logarithmic-Sobolev inequality or Poincar\'e inequality. Rather than…

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…

We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$,…