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Whereas diverse variations of diffusion models exist, extending the linear diffusion into a nonlinear diffusion process is investigated by very few works. The nonlinearity effect has been hardly understood, but intuitively, there would be…

We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a…

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"…

The rise of digital and mobile communications has recently made the world more connected and networked, resulting in an unprecedented volume of data flowing between sources, data centers, or processes. While these data may be processed in a…

In this paper, we analyze the effects of random sampling on adaptive diffusion networks. These networks consist in a collection of nodes that can measure and process data, and that can communicate with each other to pursue a common goal of…

A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

In this paper, partition-based distributed state estimation of general linear systems is considered. A distributed moving horizon state estimation scheme is developed via decomposing the entire system model into subsystem models and…

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size $N$ into $m$ machines, and estimates a local sparse LDA…

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational…

Diffusion learning is a framework that endows edge devices with advanced intelligence. By processing and analyzing data locally and allowing each agent to communicate with its immediate neighbors, diffusion effectively protects the privacy…

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Hiding data using neural networks (i.e., neural steganography) has achieved remarkable success across both discriminative classifiers and generative adversarial networks. However, the potential of data hiding in diffusion models remains…

The Langevin algorithm is a classic method for sampling from a given pdf in a real space. In its basic version, it only requires knowledge of the gradient of the log-density, also called the score function. However, in deep learning, it is…

A new reweighted l1-norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel…

A distributed average consensus algorithm robust to a wide range of impulsive channel noise distributions is proposed. This work is the first of its kind in the literature to propose a consensus algorithm which relaxes the requirement of…

In many fields, and especially in the medical and social sciences and in recommender systems, data are gathered through clinical studies or targeted surveys. Participants are generally reluctant to respond to all questions in a survey or…