Related papers: Analysis of Diffusion Models for Manifold Data

Diffusion models have been widely used in time series and spatio-temporal data, enhancing generative, inferential, and downstream capabilities. These models are applied across diverse fields such as healthcare, recommendation, climate,…

Diffusion-based editing has rapidly evolved from curated inpainting tools into general-purpose editors spanning text-guided instruction following, mask-localized edits, drag-based geometric manipulation, exemplar transfer, and training-free…

We address the problem of data augmentation in a rotating turbulence set-up, a paradigmatic challenge in geophysical applications. The goal is to reconstruct information in two-dimensional (2D) cuts of the three-dimensional flow fields,…

Diffusion generative models transform noise into data by inverting a process that progressively adds noise to data samples. Inspired by concepts from the renormalization group in physics, which analyzes systems across different scales, we…

Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This paper provides an integrated perspective on generative…

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution.…

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…

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…

Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…

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…

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

The evolutionary processes of complex systems contain critical information regarding their functional characteristics. The generation time of edges provides insights into the historical evolution of various networked complex systems, such…

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…

This study investigates human-computer interface generation based on diffusion models to overcome the limitations of traditional template-based design and fixed rule-driven methods. It first analyzes the key challenges of interface…

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…

Estimating the counterfactual outcome of treatment is essential for decision-making in public health and clinical science, among others. Often, treatments are administered in a sequential, time-varying manner, leading to an exponentially…

We provide an overview of the diffusion model as a method to generate new samples. Generative models have been recently adopted for tasks such as art generation (Stable Diffusion, Dall-E) and text generation (ChatGPT). Diffusion models in…

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…