Related papers: Heavy-Tailed Diffusion Models
Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity. This motivation is…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Score-based generative models (SGMs) have achieved remarkable empirical success, motivating their application to a broad range of data distributions. However, extending them to heavy-tailed targets remains a largely open problem. Although…
Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes,…
Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of…
Score-based diffusion models have become a powerful framework for generative modeling, with score estimation as a central statistical bottleneck. Existing guarantees for score estimation largely focus on light-tailed targets or rely on…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
Diffusion-based models have shown the merits of generating high-quality visual data while preserving better diversity in recent studies. However, such observation is only justified with curated data distribution, where the data samples are…
Exploring noise distributions beyond Gaussian in diffusion models remains an open challenge. While Gaussian-based models succeed within a unified SDE framework, recent studies suggest that heavy-tailed noise distributions, like…
We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics.…
Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly…
The variational autoencoder (VAE) typically employs a standard normal prior as a regularizer for the probabilistic latent encoder. However, the Gaussian tail often decays too quickly to effectively accommodate the encoded points, failing to…
Recent advancements in generative modeling, particularly diffusion models, have opened new directions for time series modeling, achieving state-of-the-art performance in forecasting and synthesis. However, the reliance of diffusion-based…
Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
Among likelihood-based approaches for deep generative modelling, variational autoencoders (VAEs) offer scalable amortized posterior inference and fast sampling. However, VAEs are also more and more outperformed by competing models such as…
Climate change is intensifying rainfall extremes, making high-resolution precipitation projections crucial for society to better prepare for impacts such as flooding. However, current Global Climate Models (GCMs) operate at spatial…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a class-balanced training distribution. In real-world settings, multi-class data often…
Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises"…