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Diffusion magnetic resonance imaging datasets suffer from low Signal-to-Noise Ratio, especially at high b-values. Acquiring data at high b-values contains relevant information and is now of great interest for microstructural and…

Inverse problems generally require a regularizer or prior for a good solution. A recent trend is to train a convolutional net to denoise images, and use this net as a prior when solving the inverse problem. Several proposals depend on a…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation,…

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underlying noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…

In diverse microscopy modalities, sensors measure only real-valued intensities. Additionally, the sensor readouts are affected by Poissonian-distributed photon noise. Traditional restoration algorithms typically aim to minimize the mean…

The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image.…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective…

Population dynamics is the study of temporal and spatial variation in the size of populations of organisms and is a major part of population ecology. One of the main difficulties in analyzing population dynamics is that we can only obtain…

The pose-guided person image generation task requires synthesizing photorealistic images of humans in arbitrary poses. The existing approaches use generative adversarial networks that do not necessarily maintain realistic textures or need…

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…

We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…

The use of dual system estimation (DSE) is heavily used in Census Bureau operations. With DSE methods, it is important to implement methods to infer the population size among those with missing data from one or both data sources. The use of…