Related papers: Diffusion-PINN Sampler

Modeling dynamics in the form of partial differential equations (PDEs) is an effectual way to understand real-world physics processes. For complex physics systems, analytical solutions are not available and numerical solutions are…

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by…

Despite the recent visually-pleasing results achieved, the massive computational cost has been a long-standing flaw for diffusion probabilistic models (DPMs), which, in turn, greatly limits their applications on resource-limited platforms.…

SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…

We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce…

We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which…

We study diffusion-controlled growth of a spherical droplet with a moving boundary using a physics-informed neural network (PINN) formulation. The governing diffusion equation is coupled to the interfacial mass balance, with the droplet…

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…

Diffusion models have recently achieved remarkable performance in image super-resolution (SR), but their high computational cost limits practical deployment in remote sensing applications. To address this issue, we propose SlimDiffSR, a…

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could…

Adapting the Diffusion Probabilistic Model (DPM) for direct image super-resolution is wasteful, given that a simple Convolutional Neural Network (CNN) can recover the main low-frequency content. Therefore, we present ResDiff, a novel…

Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…

Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into…

Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…

Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with…

We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…

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…