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We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Real-world data often has a long-tailed distribution, where the scarcity of tail samples significantly limits the model's generalization ability. Denoising Diffusion Probabilistic Models (DDPM) are generative models based on stochastic…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
In many real-world applications, from robotics to pedestrian trajectory prediction, there is a need to predict multiple real-valued outputs to represent several potential scenarios. Current deep learning techniques to address…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
Nanoscopic diffusion at surfaces normally takes place when an adsorbate jumps from one adsorption site to the other. Jump diffusion can be measured via quasi-elastic scattering experiments, and the results can often be interpreted in terms…
Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
A survey is given on asymptotic diffusion coefficients of particles in lattices with random transition rates. Exact and approximate results for single particles are reviewed. A recent exact expression in $d = 1$ which includes occupation…
While semiconductor electronics is at heart of modern world, and now uses 5nm or smaller processes of single atoms, it seems there are missing models of actual electron currents in these scales - which could help with more conscious design…
In molecular dynamics (MD) simulations, accessing transition probabilities between states is crucial for understanding kinetic information, such as reaction paths and rates. However, standard MD simulations are hindered by the capacity to…
Diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations and the expression for the passing probability is obtained exactly. The passing probability is…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of $n$ sites. It is partially…
The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…
Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…
Diffusion probabilistic models have achieved remarkable success in generative tasks across diverse data types. While recent studies have explored alternative degradation processes beyond Gaussian noise, this paper bridges two key diffusion…
Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how the distribution of a biomarker, such as glucose, changes over…
A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010) [Asimit, V., Furman, E. and Vernic, R. (2010) On a…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…