Related papers: The Hidden Linear Structure in Score-Based Models …

Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…

Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…

In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central…

Computational sampling has been central to the sciences since the mid-20th century. While machine-learning-based approaches have recently enabled major advances, their behavior remains poorly understood, with limited theoretical control…

Recent advances in generative models have made exploring design spaces easier for de novo molecule generation. However, popular generative models like GANs and normalizing flows face challenges such as training instabilities due to…

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…

Diffusion models have shown an impressive ability to model complex data distributions, with several key advantages over GANs, such as stable training, better coverage of the training distribution's modes, and the ability to solve inverse…

The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…

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…

This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…

The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…

Score-based diffusion models are a powerful class of generative models, widely utilized across diverse domains. Despite significant advancements in large-scale tasks such as text-to-image generation, their application to constrained domains…

We propose an efficient framework for amortized conditional inference by leveraging exact conditional score-guided diffusion models to train a non-reversible neural network as a conditional generative model. Traditional normalizing flow…

We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptions, we establish Lipschitz estimates that directly support…

The remarkable performance of deep neural networks depends on the availability of massive labeled data. To alleviate the load of data annotation, active deep learning aims to select a minimal set of training points to be labelled which…