Related papers: New algorithms for sampling and diffusion models

Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

This paper develops a rigorous probabilistic framework that extends denoising diffusion models to the setting of noncommutative random variables. Building on Voiculescu's theory of free entropy and free Fisher information, we formulate…

Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs),…

A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is…

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving…

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational…

We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies…

We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…

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…

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).…

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…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Strong generative models can accurately learn channel distributions. This could save recurring costs for physical measurements of the channel. Moreover, the resulting differentiable channel model supports training neural encoders by…

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining…

This paper proposes a supervised training algorithm for learning stochastic resource allocation policies with generative diffusion models (GDMs). We formulate the allocation problem as the maximization of an ergodic utility function subject…

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Recent success of diffusion models has inspired a surge of interest in developing sampling techniques using reverse diffusion processes. However, accurately estimating the drift term in the reverse stochastic differential equation (SDE)…

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it.…