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Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

How do score-based generative models (SBMs) learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature…

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or…

Score-based generative models (SGMs) need to approximate the scores $\nabla \log p_t$ of the intermediate distributions as well as the final distribution $p_T$ of the forward process. The theoretical underpinnings of the effects of these…

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…

We present a concise derivation for several influential score-based diffusion models that relies on only a few textbook results. Diffusion models have recently emerged as powerful tools for generating realistic, synthetic signals --…

We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via stochastic or deterministic dynamics. We present a unified framework in which diffusion models,…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive…

In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…

We present Acc3D to tackle the challenge of accelerating the diffusion process to generate 3D models from single images. To derive high-quality reconstructions through few-step inferences, we emphasize the critical issue of regularizing the…

Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…

Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…

Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the…

This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectation involving the data distribution and the forward diffusion.…

Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…