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Sampling algorithms play an important role in controlling the quality and runtime of diffusion model inference. In recent years, a number of works~\cite{chen2023sampling,chen2023ode,benton2023error,lee2022convergence} have proposed schemes…

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…

Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

While gradient-based discrete samplers are effective in sampling from complex distributions, they are susceptible to getting trapped in local minima, particularly in high-dimensional, multimodal discrete distributions, owing to the…

Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that is not fully represented by one generative model. We introduce Generative Gibbs for…

This paper proposes a novel Bayesian framework for solving Poisson inverse problems by devising a Monte Carlo sampling algorithm which accounts for the underlying non-Euclidean geometry. To address the challenges posed by the Poisson…

Gibbs sampling repeatedly samples from the conditional distribution of one variable, x_i, given other variables, either choosing i randomly, or updating sequentially using some systematic or random order. When x_i is discrete, a Gibbs…

Channel modelling is essential to designing modern wireless communication systems. The increasing complexity of channel modelling and the cost of collecting high-quality wireless channel data have become major challenges. In this paper, we…

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…

Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…

The Poisson-sampling technique eliminates dependencies among symbol appearances in a random sequence. It has been used to simplify the analysis and strengthen the performance guarantees of randomized algorithms. Applying this method to…

Herding is a technique to sequentially generate deterministic samples from a probability distribution. In this work, we propose a continuous herded Gibbs sampler that combines kernel herding on continuous densities with the Gibbs sampling…

A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to…

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…

We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…

We investigate a weighted Multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in~[Lemaire-Pag\`es, 2013] for regular Monte Carlo simulation. In a…

Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current…

Diffusion models are distinguished by their exceptional generative performance, particularly in producing high-quality samples through iterative denoising. While current theory suggests that the number of denoising steps required for…

We present a diffusion-based image morphing approach with perceptually-uniform sampling (IMPUS) that produces smooth, direct and realistic interpolations given an image pair. The embeddings of two images may lie on distinct conditioned…