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Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

This paper presents a shape-theoretic framework for dynamical analysis of nonlinear dynamical systems which appear frequently in several video-based inference tasks. Traditional approaches to dynamical modeling have included linear and…

We use hierarchical procedural rules for the generation of control maps within the stable diffusion framework to produce photo-realistic architectural facade images. Starting from a single input image and its segmentation, we apply an…

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium…

Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these…

In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…

The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…

Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either…

We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…

A possibility to use an integral operator for establishing the link between physical and structural levels of materials in modeling diffusion processes is considered. We show how to perform the transition from the stochastic description of…

Diffusion Probabilistic Methods are employed for state-of-the-art image generation. In this work, we present a method for extending such models for performing image segmentation. The method learns end-to-end, without relying on a…

We introduce the Quartet of Diffusions, a structure-aware point cloud generation framework that explicitly models part composition and symmetry. Unlike prior methods that treat shape generation as a holistic process or only support part…

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant).…

A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…

The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…