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This paper explores the utility of diffusion-based models for anomaly detection, focusing on their efficacy in identifying deviations in both compact and high-resolution datasets. Diffusion-based architectures, including Denoising Diffusion…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
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.…
Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated…
The article demonstrates uncommon manifestation of spatial dispersion in low refractive index contrast 3D periodic dielectric composites with periods of about one tenth of the wavelength. First principles simulations by the well established…
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…
L\'{e}vy flight models whose jumps have infinite moments are mathematically used to describe the superdiffusion in complex systems. Exponentially tempering the Levy measure of L\'{e}vy flights leads to the tempered stable L\'{e}vy processes…
Diffusion Models achieve state-of-the-art performance in generating new samples but lack a low-dimensional latent space that encodes the data into editable features. Inversion-based methods address this by reversing the denoising…
We derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random shuffling within the $f$-DP framework. Our analysis covers the regime $\sigma \geq…
A diffusion molecular channel is a channel with memory, as molecules released into the medium hit the receptors after a random delay. Coding over the diffusion channel is performed by choosing the type, intensity, or the released time of…
Designing resource allocation strategies for power constrained sensor network in the presence of correlated data often gives rise to intractable problem formulations. In such situations, applying well-known strategies derived from…
Diffusion pore imaging is an extension of diffusion-weighted nuclear magnetic resonance imaging enabling the direct measurement of the shape of arbitrarily formed, closed pores by probing diffusion restrictions using the motion of…
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we…
Diffusion MRI (dMRI) provides contrast that reflect diffusing spins' interactions with microstructural features of biological systems, but its specificity remains limited due to the ambiguity of its relation to the underlying…
We propose a compressive spectral collocation method for the numerical approximation of Partial Differential Equations (PDEs). The approach is based on a spectral Sturm-Liouville approximation of the solution and on the collocation of the…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
We address the discretization of two-phase Darcy flows in a fractured and deformable porous medium, including frictional contact between the matrix-fracture interfaces. Fractures are described as a network of planar surfaces leading to the…
Diffusion probabilistic models (DPMs) have become a popular approach to conditional generation, due to their promising results and support for cross-modal synthesis. A key desideratum in conditional synthesis is to achieve high…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive (AR) models for language modeling, allowing flexible generation order and parallel generation of multiple tokens. However, this flexibility…