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We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…
Diffusion models have become widely popular for automated floorplan generation, producing highly realistic layouts conditioned on user-defined constraints. However, optimizing for perceptual metrics such as the Fr\'echet Inception Distance…
Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…
Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing…
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for discrete diffusion models remains less well-understood. In…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Discrete diffusion models have recently gained significant prominence in applications involving natural language and graph data. A key factor influencing their effectiveness is the efficiency of discretized samplers. Among these,…
Diffusion probabilistic models (DPMs) have shown remarkable results on various image synthesis tasks such as text-to-image generation and image inpainting. However, compared to other generative methods like VAEs and GANs, DPMs lack a…
A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…
Latent diffusion models have emerged as the dominant framework for high-fidelity and efficient image generation, owing to their ability to learn diffusion processes in compact latent spaces. However, while previous research has focused…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…
A method for the quantification of acoustophoretic separation and dispersion for microparticle populations featuring continuously distributed physical parameters is presented. The derivation of the method starts by (i)~considering the…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…
Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation, and…
In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass \&…
We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…