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Long-tailed imbalance distribution is a common issue in practical computer vision applications. Previous works proposed methods to address this problem, which can be categorized into several classes: re-sampling, re-weighting, transfer…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

This work presents a distributed algorithm for nonlinear adaptive learning. In particular, a set of nodes obtain measurements, sequentially one per time step, which are related via a nonlinear function; their goal is to collectively…

Learning complex distributions is a fundamental challenge in contemporary applications. Shen and Meinshausen (2024) introduced engression, a generative approach based on scoring rules that maps noise (and covariates, if available) directly…

Diffusion models (DMs) are capable of generating remarkably high-quality samples by iteratively denoising a random vector, a process that corresponds to moving along the probability flow ordinary differential equation (PF ODE).…

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that \emph{the same noise level on a higher…

Advances in endoscopy use in surgeries face challenges like inadequate lighting. Deep learning, notably the Denoising Diffusion Probabilistic Model (DDPM), holds promise for low-light image enhancement in the medical field. However, DDPMs…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a Markov Chain Monte Carlo (MCMC) algorithm, we show that the…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…

Diffusion Large Language Models (DLLMs) promise fast non-autoregressive inference but suffer a severe quality-speed trade-off in parallel decoding. This stems from the ''combinatorial contradiction'' phenomenon, where parallel tokens form…

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…

While Diffusion Language Models (DLMs) are theoretically well-suited for iterative refinement due to their non-causal structure, they often fail to reliably revise incorrect tokens in practice. The key challenge lies in the model's…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

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…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Diffusion-based methods demonstrate significant potential for remote sensing image super-resolution at large scaling factors, particularly in reference-based super-resolution (RefSR) where high-resolution reference images provide critical…

Recently, text-to-image diffusion models become a new paradigm in image processing fields, including content generation, image restoration and image-to-image translation. Given a target prompt, Denoising Diffusion Probabilistic Models…

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods…