Related papers: Elucidating the solution space of extended reverse…

Tokenizers are a key component of state-of-the-art generative image models, extracting the most important features from the signal while reducing data dimension and redundancy. Most current tokenizers are based on KL-regularized variational…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Recently, a series of diffusion-aware distillation algorithms have emerged to alleviate the computational overhead associated with the multi-step inference process of Diffusion Models (DMs). Current distillation techniques often dichotomize…

Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

Diffusion Models (DMs) have achieved great success in image generation and other fields. By fine sampling through the trajectory defined by the SDE/ODE solver based on a well-trained score model, DMs can generate remarkable high-quality…

Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…

Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_{\theta}(X_0|y)$, with a predefined diffusion model $p_{\theta}(X_0)$, an operator $f(\cdot)$, and a measurement $y=f(x'_0)$ derived from an unknown…

Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…

Diffusion-based generative models have demonstrated their powerful performance across various tasks, but this comes at a cost of the slow sampling speed. To achieve both efficient and high-quality synthesis, various distillation-based…

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based…

Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…

Ordinary differential equations (ODEs) are a mathematical model used in many application areas such as climatology, bioinformatics, and chemical engineering with its intuitive appeal to modeling. Despite ODE's wide usage in modeling, the…

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…

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic…

Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling…

Diffusion-based image super-resolution (SR) methods have shown promise in reconstructing high-resolution images with fine details from low-resolution counterparts. However, these approaches typically require tens or even hundreds of…