Related papers: Tweedie's Formulae and Diffusion Generative Models…

Optimal extraction of cosmological information from observations of the Cosmic Microwave Background critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the…

We introduce a general framework for generating diverse visual content, including ambiguous images, panorama images, mesh textures, and Gaussian splat textures, by synchronizing multiple diffusion processes. We present exhaustive…

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…

Score-based stochastic denoising models have recently been demonstrated as powerful machine learning tools for conditional and unconditional image generation. The existing methods are based on a forward stochastic process wherein the…

The Tweedie generalized linear models are commonly applied in the insurance industry to analyze semicontinuous claim data. For better prediction of the aggregated claim size, the mean and dispersion of the Tweedie model are often estimated…

We adopt Gaussian Processes (GPs) as latent functions for probabilistic forecasting of intermittent time series. The model is trained in a Bayesian framework that accounts for the uncertainty about the latent function. We couple the latent…

Diffusion models (DMs) excel in unconditional generation, as well as on applications such as image editing and restoration. The success of DMs lies in the iterative nature of diffusion: diffusion breaks down the complex process of mapping…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Generating graph-structured data is crucial in applications such as molecular generation, knowledge graphs, and network analysis. However, their discrete, unordered nature makes them difficult for traditional generative models, leading to…

Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…

Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…

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…

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

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…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…