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Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

Diffusion probabilistic models have demonstrated an outstanding capability to model natural images and raw audio waveforms through a paired diffusion and reverse processes. The unique property of the reverse process (namely, eliminating…

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…

Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly…

Diffusion models have demonstrated impressive capabilities in synthesizing diverse content. However, despite their high-quality outputs, these models often perpetuate social biases, including those related to gender and race. These biases…

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"…

Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

Diffusion models generate samples by incrementally reversing a process that turns data into noise. We show that when the step size goes to zero, the reversed process is invariant to the distribution of these increments. This reveals a…

Diffusion models have achieved remarkable success in generative modeling, yet how to effectively adapt large pretrained models to new tasks remains challenging. We revisit the reconstruction behavior of diffusion models during denoising to…

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…

Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…

Synthetic samples from diffusion models are promising for leveraging in training discriminative models as replications of real training datasets. However, we found that the synthetic datasets degrade classification performance over real…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Recently, diffusion models have shown remarkable results in image synthesis by gradually removing noise and amplifying signals. Although the simple generative process surprisingly works well, is this the best way to generate image data? For…

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

The Transformer model has shown leading performance in time series forecasting. Nevertheless, in some complex scenarios, it tends to learn low-frequency features in the data and overlook high-frequency features, showing a frequency bias.…