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Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…

Particle filters are a group of algorithms to solve inverse problems through statistical Bayesian methods when the model does not comply with the linear and Gaussian hypothesis. Particle filters are used in domains like data assimilation,…

The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive…

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

As diffusion models become increasingly popular, the misuse of copyrighted and private images has emerged as a major concern. One promising solution to mitigate this issue is identifying the contribution of specific training samples in…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

In many real-world scenarios, we often deal with streaming data that is sequentially collected over time. Due to the non-stationary nature of the environment, the streaming data distribution may change in unpredictable ways, which is known…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Adversarial Imitation Learning is traditionally framed as a two-player zero-sum game between a learner and an adversarially chosen cost function, and can therefore be thought of as the sequential generalization of a Generative Adversarial…

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…

Data assimilation combines information from physical observations and numerical simulation results to obtain better estimates of the state and parameters of a physical system. A wide class of physical systems of interest have solutions that…

Domain Adaptation(DA) for dense prediction tasks is an important topic, which enhances the dense prediction model's performance when tested on its unseen domain. Recently, with the development of Diffusion-based Dense Prediction (DDP)…

In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

This paper proposes a new unsupervised audio-visual speech enhancement (AVSE) approach that combines a diffusion-based audio-visual speech generative model with a non-negative matrix factorization (NMF) noise model. First, the diffusion…

The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…