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Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

Idempotent Generative Networks (IGNs) are deep generative models that also function as local data manifold projectors, mapping arbitrary inputs back onto the manifold. They are trained to act as identity operators on the data and as…

Generative models, such as Variational Auto-Encoder (VAE) and Generative Adversarial Network (GAN), have been successfully applied in sequential recommendation. These methods require sampling from probability distributions and adopt…

Diffusion models are powerful generative models that achieve state-of-the-art performance in image synthesis. However, training them demands substantial amounts of data and computational resources. Continual learning would allow for…

The ability of generative models to accurately fit data distributions has resulted in their widespread adoption and success in fields such as computer vision and natural language processing. In this chapter, we provide a brief overview of…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Generative models such as Generative Adversarial Networks (GANs) and Variational Auto-Encoders (VAEs) are widely utilized to model the generative process of user interactions. However, these generative models suffer from intrinsic…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

Recent advances in deep learning have enabled the generation of realistic data by training generative models on large datasets of text, images, and audio. While these models have demonstrated exceptional performance in generating novel and…

Diffusion models (DMs) have achieved state-of-the-art performance on various generative tasks such as image synthesis, text-to-image, and text-guided image-to-image generation. However, the more powerful the DMs, the more harmful they…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

Since most inverse problems arising in scientific and engineering applications are ill-posed, prior information about the solution space is incorporated, typically through regularization, to establish a well-posed problem with a unique…

In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Deep learning has become a popular tool for medical image analysis, but the limited availability of training data remains a major challenge, particularly in the medical field where data acquisition can be costly and subject to privacy…

In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex,…

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…