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Recently, a variety of regularization techniques have been widely applied in deep neural networks, such as dropout, batch normalization, data augmentation, and so on. These methods mainly focus on the regularization of weight parameters to…
We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding…
In decentralized optimization, several nodes connected by a network collaboratively minimize some objective function. For minimization of Lipschitz functions lower bounds are known along with optimal algorithms. We study a specific class of…
World models aim to capture the states and dynamics of an environment in a compact latent space. Moreover, using Boolean state representations is particularly useful for search heuristics and symbolic reasoning and planning. Existing…
Image restoration aims to enhance low quality images, producing high quality images that exhibit natural visual characteristics and fine semantic attributes. Recently, the diffusion model has emerged as a powerful technique for image…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
Many challenging image processing tasks can be described by an ill-posed linear inverse problem: deblurring, deconvolution, inpainting, compressed sensing, and superresolution all lie in this framework. Traditional inverse problem solvers…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
Diffusion models (DMs) are generative models that learn to synthesize images from Gaussian noise. DMs can be trained to do a variety of tasks such as image generation and image super-resolution. Researchers have made significant…
Distributed optimization methods with local updates have recently attracted a lot of attention due to their potential to reduce the communication cost of distributed methods. In these algorithms, a collection of nodes performs several local…
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
We seek to give users precise control over diffusion-based image generation by modeling complex scenes as sequences of layers, which define the desired spatial arrangement and visual attributes of objects in the scene. Collage Diffusion…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…
Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible…