Related papers: Face Super-Resolution Using Stochastic Differentia…

Diffusion models (DMs) are generative models that learn to synthesize images from Gaussian noise. DMs can be trained to do a variety of tasks such as image generation and image super-resolution. Researchers have made significant…

Diffusion models represent the state-of-the-art in generative modeling. Due to their high training costs, many works leverage pre-trained diffusion models' powerful representations for downstream tasks, such as face super-resolution (FSR),…

Super-resolution (SR) is by definition ill-posed. There are infinitely many plausible high-resolution variants for a given low-resolution natural image. Most of the current literature aims at a single deterministic solution of either high…

Diffusion bridge models have demonstrated promising performance in conditional image generation tasks, such as image restoration and translation, by initializing the generative process from corrupted images instead of pure Gaussian noise.…

We develop a novel approach towards causal inference. Rather than structural equations over a causal graph, we learn stochastic differential equations (SDEs) whose stationary densities model a system's behavior under interventions. These…

Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…

We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…

Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization methods exist for such problems, characterizing their…

Diffusion models have gained significant popularity in the field of image-to-image translation. Previous efforts applying diffusion models to image super-resolution (SR) have demonstrated that iteratively refining pure Gaussian noise using…

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…

This is an expository article on the score-based diffusion models, with a particular focus on the formulation via stochastic differential equations (SDE). After a gentle introduction, we discuss the two pillars in the diffusion modeling --…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are…

Synthesizing face images from monochrome sketches is one of the most fundamental tasks in the field of image-to-image translation. However, it is still challenging to (1)~make models learn the high-dimensional face features such as geometry…

This paper considers the problem of utilizing a large-scale text-to-image diffusion model to tackle the challenging Inexact Segmentation (IS) task. Unlike traditional approaches that rely heavily on discriminative-model-based paradigms or…

We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given…

Recent years have witnessed the prosperity of reference-based image super-resolution (Ref-SR). By importing the high-resolution (HR) reference images into the single image super-resolution (SISR) approach, the ill-posed nature of this…

Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…