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Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
Generative models have attracted significant interest due to their ability to handle uncertainty by learning the inherent data distributions. However, two prominent generative models, namely Generative Adversarial Networks (GANs) and…
Learning models with categorical variables requires optimizing expectations over discrete distributions, a setting in which stochastic gradient-based optimization is challenging due to the non-differentiability of categorical sampling. A…
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized…
Edge detection is typically viewed as a pixel-level classification problem mainly addressed by discriminative methods. Recently, generative edge detection methods, especially diffusion model based solutions, are initialized in the edge…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average…
Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
The vast applications of deep generative models are anchored in three core capabilities -- generating new instances, reconstructing inputs, and learning compact representations -- across various data types, such as discrete text/protein…
Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional complex systems predict future states individually. This approach struggles to model complex temporal dependencies and fails to…
Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…
Diffusion models (DMs) excel in image generation but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers for DMs accelerate denoising inference, they often lack theoretical foundations in…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…