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Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…

Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…

Weakly supervised semantic segmentation (WSSS) methods using class labels often rely on class activation maps (CAMs) to localize objects. However, traditional CAM-based methods struggle with partial activations and imprecise object…

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…

Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…

Full waveform inversion (FWI) is an advanced seismic inversion technique for quantitatively estimating subsurface properties. However, with FWI, it is hard to converge to a geologically-realistic subsurface model. Thus, we propose a…

Different rain models and novel network structures have been proposed to remove rain streaks from single rainy images. In this work, we bring attention to the intrinsic priors and multi-scale features of the rainy images, and develop…

Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…

We present a multi-sensor Bayesian passive microwave retrieval algorithm for flood inundation mapping at high spatial and temporal resolutions. The algorithm takes advantage of observations from multiple sensors in optical, short-infrared,…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

Recent advancements in image restoration increasingly employ conditional latent diffusion models (CLDMs). While these models have demonstrated notable performance improvements in recent years, this work questions their suitability for IR…

As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we explore empirically the sampling challenges this approach offers which have to do with the strong correlations and multi-modality of the…

The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…

The study of turbulent flows calls for measurements with high resolution both in space and in time. We propose a new approach to reconstruct High-Temporal-High-Spatial resolution velocity fields by combining two sources of information that…

Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…

Data assimilation is a fundamental task in updating forecasting models upon observing new data, with applications ranging from weather prediction to online reinforcement learning. Deep generative forecasting models (DGFMs) have shown…