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Generative models capture the true distribution of data, yielding semantically rich representations. Denoising diffusion models (DDMs) exhibit superior generative capabilities, though efficient representation learning for them are lacking.…

Text-conditioned image generation models have recently shown immense qualitative success using denoising diffusion processes. However, unlike discriminative vision-and-language models, it is a non-trivial task to subject these…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating…

The variational autoencoder (VAE) is a popular model for density estimation and representation learning. Canonically, the variational principle suggests to prefer an expressive inference model so that the variational approximation is…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

While deep generative models~(DGMs) have demonstrated remarkable success in capturing complex data distributions, they consistently fail to learn constraints that encode domain knowledge and thus require constraint integration. Existing…

Deep neural networks (DNNs) trained for image denoising are able to generate high-quality samples with score-based reverse diffusion algorithms. These impressive capabilities seem to imply an escape from the curse of dimensionality, but…

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…

Diffusion models have recently emerged as powerful generative models in medical imaging. However, it remains a major challenge to combine these data-driven models with domain knowledge to guide brain imaging problems. In neuroimaging,…

Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets…

Full characterization of the spectral behavior of generative models based on neural networks remains an open issue. Recent research has focused heavily on generative adversarial networks and the high-frequency discrepancies between real and…

With the rapid evolution of synthetic media, Image Manipulation Localization (IML) has emerged as a critical component in multimedia forensics for ensuring the integrity of digital content. However, generalization remains a core challenge,…

We introduce a framework for analyzing and designing EIS inversion algorithms. Our framework stems from the observation of four features common to well-defined EIS inversion algorithms, namely (1) the representation of unknown…

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned…

Diffusion autoencoders (DAEs) are typically formulated as a noise prediction model and trained with a linear-$\beta$ noise schedule that spends much of its sampling steps at high noise levels. Because high noise levels are associated with…

Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…