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Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…

Global Navigation Satellite Systems (GNSS) are vital for reliable urban positioning. However, multipath and non-line-of-sight reception often introduce large measurement errors that degrade accuracy. Learning-based methods for predicting…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

Diffusion probabilistic models (DPMs) have achieved impressive success in visual generation. While, they suffer from slow inference speed due to iterative sampling. Employing fewer sampling steps is an intuitive solution, but this will also…

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…

We propose a straightforward and effective method for discretizing multi-dimensional diffusion processes as an extension of Milstein scheme. The new scheme is explicitly given and can be simulated using Gaussian variates, requiring the same…

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy…

We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say…

We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments,…

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…

Diffusion models that can generate high-quality data from randomly sampled Gaussian noises have become the mainstream generative method in both academia and industry. Are randomly sampled Gaussian noises equally good for diffusion models?…

Forecasting over graph-structured sensor networks demands models that capture both deterministic spatial trends and stochastic variability, while remaining efficient enough for repeated inference as new observations arrive. We propose…

Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…

Typically when designing distributed controllers it is assumed that the state-space model of the plant consists of sparse matrices. However, in the discrete-time setting, if one begins with a continuous-time model, the discretization…

The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…

Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory…

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…

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,…