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Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

Learning from a large corpus of data, pre-trained models have achieved impressive progress nowadays. As popular generative pre-training, diffusion models capture both low-level visual knowledge and high-level semantic relations. In this…

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time…

Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…

Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…

Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…

Diffusion models have risen to prominence in time series forecasting, showcasing their robust capability to model complex data distributions. However, their effectiveness in deterministic predictions is often constrained by instability…

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.…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and…

Training data has been proven to be one of the most critical components in training generative AI. However, obtaining high-quality data remains challenging, with data privacy issues presenting a significant hurdle. To address the need for…

It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…

Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…

This paper demonstrates how to use generative models trained for image synthesis as tools for visual data mining. Our insight is that since contemporary generative models learn an accurate representation of their training data, we can use…

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…