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Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Diffusion models (DMs) excel in photorealism, image editing, and solving inverse problems, aided by classifier-free guidance and image inversion techniques. However, rectified flow models (RFMs) remain underexplored for these tasks.…

Missing value imputation in machine learning is the task of estimating the missing values in the dataset accurately using available information. In this task, several deep generative modeling methods have been proposed and demonstrated…

Diffusion-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of…

Diffusion models have recently shown great promise for generative modeling, outperforming GANs on perceptual quality and autoregressive models at density estimation. A remaining downside is their slow sampling time: generating high quality…

This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…

Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. In this work we propose to extend this methodology to learn generative models over functional spaces. To…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

Speech super-resolution (SR) is the task that restores high-resolution speech from low-resolution input. Existing models employ simulated data and constrained experimental settings, which limit generalization to real-world SR. Predictive…

Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…

Graph generative models are essential across diverse scientific domains by capturing complex distributions over relational data. Among them, graph diffusion models achieve superior performance but face inefficient sampling and limited…

Accurately predicting 3D occupancy grids from visual inputs is critical for autonomous driving, but current discriminative methods struggle with noisy data, incomplete observations, and the complex structures inherent in 3D scenes. In this…

Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…

We propose the Value Gradient Sampler (VGS), a diffusion sampler parameterized by value functions. VGS generates samples from an unnormalized target density (i.e., energy) by evolving randomly initialized particles along the gradient of the…

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…

Diffusion models have emerged as powerful deep generative techniques, producing high-quality and diverse samples in applications in various domains including audio. While existing reviews provide overviews, there remains limited in-depth…

These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…