Related papers: Learning Interpretable PDE Representations for Gen…

Obtaining accurate estimates of uncertainty in climate scenarios often requires generating large ensembles of high-resolution climate simulations, a computationally expensive and memory intensive process. To address this challenge, we train…

While latent diffusion models (LDMs), such as Stable Diffusion, are designed for high-resolution (HR) image generation, they often struggle with significant structural distortions when generating images at resolutions higher than their…

Internal activations of diffusion models encode rich semantic information, but interpreting such representations remains challenging. While Sparse Autoencoders (SAEs) have shown promise in disentangling latent representations, existing…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative…

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…

While diffusion models excel at generating high-quality samples, their latent variables typically lack semantic meaning and are not suitable for representation learning. Here, we propose InfoDiffusion, an algorithm that augments diffusion…

Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…

In the era of generative AI, deep generative models (DGMs) with latent representations have gained tremendous popularity. Despite their impressive empirical performance, the statistical properties of these models remain underexplored. DGMs…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Physics-informed diffusion models typically enforce PDE constraints only on final outputs, leaving intermediate representations unconstrained and prone to shortcut learning under shifted boundary conditions. We introduce **REPA-P**, a…

Counterfactual explanations have emerged as a promising method for elucidating the behavior of opaque black-box models. Recently, several works leveraged pixel-space diffusion models for counterfactual generation. To handle noisy,…

Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn…

Due to limitations such as geographic, physical, or economic factors, collected seismic data often have missing traces. Traditional seismic data reconstruction methods face the challenge of selecting numerous empirical parameters and…

Current perceptive models heavily depend on resource-intensive datasets, prompting the need for innovative solutions. Leveraging recent advances in diffusion models, synthetic data, by constructing image inputs from various annotations,…

Latent feature representation methods play an important role in the dimension reduction and statistical modeling of high-dimensional complex data objects. However, existing approaches to assess the quality of these methods often rely on…