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We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…

We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…

The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where…

Addressing decision-making problems using sequence modeling to predict future trajectories shows promising results in recent years. In this paper, we take a step further to leverage the sequence predictive method in wider areas such as…

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary…

Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…

Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially…

We develop an analytically tractable single-step diffusion model based on a linear denoiser and present an explicit formula for the Kullback-Leibler divergence between the generated and sampling distribution, taken to be isotropic Gaussian,…

Masked discrete diffusion models (MDMs) are a promising new approach to generative modelling, offering the ability for parallel token generation and therefore greater efficiency than autoregressive counterparts. However, achieving an…

Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Deep generative models have garnered significant attention in low-level vision tasks due to their generative capabilities. Among them, diffusion model-based solutions, characterized by a forward diffusion process and a reverse denoising…

Diffusion models have been widely adopted in image generation, producing higher-quality and more diverse samples than generative adversarial networks (GANs). We introduce a latent diffusion model (LDM) for precipitation nowcasting -…

Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent…

Generative models such as Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) have shown promise in sequential recommendation tasks. However, they face challenges, including posterior collapse and limited…

In quantum many-body systems, measurements can induce qualitative new features, but their simulation is hindered by the exponential complexity involved in sampling the measurement results. We propose to use machine learning to assist the…

We present a deep generative model for unsupervised text style transfer that unifies previously proposed non-generative techniques. Our probabilistic approach models non-parallel data from two domains as a partially observed parallel…