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The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Molecular modeling, a central topic in quantum mechanics, aims to accurately calculate the properties and simulate the behaviors of molecular systems. The molecular model is governed by physical laws, which impose geometric constraints such…
In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…
Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
We tackle the task of geometric image editing, where an object within an image is repositioned, reoriented, or reshaped while preserving overall scene coherence. Previous diffusion-based editing methods often attempt to handle all relevant…
Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show…
Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models…
Generative models, particularly diffusion model, have emerged as powerful tools for sequential recommendation. However, accurately modeling user preferences remains challenging due to the noise perturbations inherent in the forward and…
Diffusion models are widely used in image generation, with most relying on noise-based corruption and denoising. A distinct branch instead uses blur as the main corruption, preserving better color budgets and multi-scale detail by providing…
In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…
Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also…
Point cloud streaming is increasingly getting popular, evolving into the norm for interactive service delivery and the future Metaverse. However, the substantial volume of data associated with point clouds presents numerous challenges,…
Diffusion models represent the state-of-the-art for solving inverse problems such as image restoration tasks. Diffusion-based inverse solvers incorporate a likelihood term to guide prior sampling, generating data consistent with the…
The development of video diffusion models unveils a significant challenge: the substantial computational demands. To mitigate this challenge, we note that the reverse process of diffusion exhibits an inherent entropy-reducing nature. Given…
Flow matching has emerged as a simulation-free alternative to diffusion-based generative modeling, producing samples by solving an ODE whose time-dependent velocity field is learned along an interpolation between a simple source…
We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…
Recent advances in meta-optics have enabled diverse functionalities in compact optical devices; however, conventional forward design approaches become inadequate as device complexity and scale grow. Inverse design offers a powerful…
In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded…
Dataset distillation compresses large datasets into compact synthetic sets with comparable performance in training models. Despite recent progress on diffusion-based distillation, this type of method typically depends on heuristic guidance…