Related papers: Guided filtering and smoothing for infinite-dimens…
We consider a design problem where experimental conditions (design points $X_i$) are presented in the form of a sequence of i.i.d.\ random variables, generated with an unknown probability measure $\mu$, and only a given proportion…
Adapting pretrained image-based diffusion models to generate temporally consistent videos has become an impactful generative modeling research direction. Training-free noise-space manipulation has proven to be an effective technique, where…
We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…
Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin…
In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) =…
Consider a multidimensional diffusion process $X=\{X\left(t\right) :t\in\lbrack0,1]\}$. Let $\varepsilon>0$ be a \textit{deterministic}, user defined, tolerance error parameter. Under standard regularity conditions on the drift and…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We study a class of deterministic flows in ${\mathbb R}^{d\times k}$, parametrized by a random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ with i.i.d. centered subgaussian entries. We characterize the asymptotic behavior of these…
Recent literature has effectively leveraged diffusion models trained on continuous variables as priors for solving inverse problems. Notably, discrete diffusion models with discrete latent codes have shown strong performance, particularly…
We introduce, test and discuss a method for classifying and clustering data modeled as directed graphs. The idea is to start diffusion processes from any subset of a data collection, generating corresponding distributions for reaching…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
Global search and optimization of long-duration, low-thrust spacecraft trajectories with the indirect method is challenging due to a complex solution space and the difficulty of generating good initial guesses for the costate variables.…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…
Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…
We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is…
We present a method to characterize the distribution of length-scales of finite, disordered patterns with, on average, radial symmetry. This method makes it possible to quantify the distribution of characteristic length scales in cases…
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).…