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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…
Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…
We introduce nested diffusion models, an efficient and powerful hierarchical generative framework that substantially enhances the generation quality of diffusion models, particularly for images of complex scenes. Our approach employs a…
The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…
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-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of…
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,…
Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…
Diffusion Models have become a cornerstone of modern generative AI for their exceptional generation quality and controllability. However, their inherent \textit{multi-step iterations} and \textit{complex backbone networks} lead to…
In recent years, generative diffusion models have achieved a rapid paradigm shift in deep generative models by showing groundbreaking performance across various applications. Meanwhile, structured data, encompassing tabular and time series…
A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of…
Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…
Generative modeling and clustering are conventionally distinct tasks in machine learning. Variational Autoencoders (VAEs) have been widely explored for their ability to integrate both, providing a framework for generative clustering.…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…