Related papers: GeoFunFlow: Geometric Function Flow Matching for I…

We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…

The inverse design of metasurfaces faces inherent challenges due to the nonlinear and highly complex relationship between geometric configurations and their electromagnetic behavior. Traditional optimization approaches often suffer from…

The Gradient Vector Flow (GVF) is a vector diffusion approach based on Partial Differential Equations (PDEs). This method has been applied together with snake models for boundary extraction medical images segmentation. The key idea is to…

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Transformer-based neural operators have emerged as promising surrogate solvers for partial differential equations, by leveraging the effectiveness of Transformers for capturing long-range dependencies and global correlations, profoundly…

Recent advances in generative modeling have substantially enhanced novel view synthesis, yet maintaining consistency across viewpoints remains challenging. Diffusion-based models rely on stochastic noise-to-data transitions, which obscure…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…

Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows,…

Inferring physical fields from sparse observations while strictly satisfying partial differential equations (PDEs) is a fundamental challenge in computational physics. Recently, deep generative models offer powerful data-driven priors for…

This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

Generative adversarial network (GAN) has been shown to be useful in various applications, such as image recognition, text processing and scientific computing, due its strong ability to learn complex data distributions. In this study, a…

Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…

In this paper we introduce CorticalFlow, a new geometric deep-learning model that, given a 3-dimensional image, learns to deform a reference template towards a targeted object. To conserve the template mesh's topological properties, we…

Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…

Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…

Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…