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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…

Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…

Automatic layout generation that can synthesize high-quality layouts is an important tool for graphic design in many applications. Though existing methods based on generative models such as Generative Adversarial Networks (GANs) and…

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…

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.…

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.…

Continuous diffusion has been the foundation of high-fidelity, controllable, and few-step generation of many data modalities such as images. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind…

Generative models can be categorized into two types: explicit generative models that define explicit density forms and allow exact likelihood inference, such as score-based diffusion models (SDMs) and normalizing flows; implicit generative…

Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…

In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…

Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…

Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a time-indexed target path by reweighting…

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated…

Climate change necessitates rapid expansion of renewable energy, with wind energy offering a scalable and low-impact solution. However, accurate prediction of wind loads and power generation remains challenging due to uncertainties in wind…

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…

Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…