Related papers: Unifying and extending Diffusion Models through PD…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

We present a conditional diffusion model for electromagnetic inverse design that generates structured media geometries directly from target differential scattering cross-section profiles, bypassing expensive iterative optimization. Our 1D…

Diffusion models have emerged as powerful generative priors for high-dimensional inverse problems, yet learning them when only corrupted or noisy observations are available remains challenging. In this work, we propose a new method for…

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…

Recent advancements in diffusion models have been effective in learning data priors for solving inverse problems. They leverage diffusion sampling steps for inducing a data prior while using a measurement guidance gradient at each step to…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Despite the growing interest in diffusion models, gaining a deep understanding of the model class remains an elusive endeavour, particularly for the uninitiated in non-equilibrium statistical physics. Thanks to the rapid rate of progress in…

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be…

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

Microstructure reconstruction, a major component of inverse computational materials engineering, is currently advancing at an unprecedented rate. While various training-based and training-free approaches are developed, the majority of…

Diffusion models can be used as learned priors for solving various inverse problems. However, most existing approaches are restricted to linear inverse problems, limiting their applicability to more general cases. In this paper, we build…

Diffusion models, initially developed for image synthesis, demonstrate remarkable generative capabilities. Recently, their application has expanded to time series forecasting (TSF), yielding promising results. Existing surveys on time…