Related papers: Unleashing High-Quality Image Generation in Diffus…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
We describe a new MCMC method optimized for the sampling of probability measures on Hilbert space which have a density with respect to a Gaussian; such measures arise in the Bayesian approach to inverse problems, and in conditioned…
We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In particular, the Euclidean Langevin Monte Carlo sampling…
By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a…
In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution…
Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications and benefit from strong theoretical guarantees. Recently, methods inspired by statistical mechanics, in…
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 research presents a novel framework for the compression and decompression of medical images utilizing the Latent Diffusion Model (LDM). The LDM represents advancement over the denoising diffusion probabilistic model (DDPM) with a…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
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…
Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be…
Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the…
Priors with non-smooth log-densities, such as the l1-prior, are widely used in Bayesian inverse problems for their sparsity-inducing properties. Existing Langevin-based sampling methods typically rely on proximal mappings or smooth…
Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
3D Gaussian Splatting (3DGS) is widely used for novel view synthesis due to its high rendering quality and fast inference time. However, 3DGS predominantly relies on first-order optimizers such as Adam, which leads to long training times.…
Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song…
The efficiency of a Markov sampler based on the underdamped Langevin diffusion is studied for high dimensional targets with convex and smooth potentials. We consider a classical second-order integrator which requires only one gradient…
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).…