Related papers: Kernel-Smoothed Scores for Denoising Diffusion: A …

Despite the widespread adoption of deterministic samplers in diffusion models (DMs), their potential limitations remain largely unexplored. In this paper, we identify collapse errors, a previously unrecognized phenomenon in ODE-based…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…

Denoising diffusion (score-based) generative models have recently achieved significant accomplishments in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data into noise and a…

Recent work has shown that diffusion models trained with the denoising score matching (DSM) objective often violate the Fokker--Planck (FP) equation that governs the evolution of the true data density. Directly penalizing these deviations…

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this…

Diffusion models (DMs) as generative priors have recently shown great potential for denoising tasks but lack theoretical understanding with respect to their mean square error (MSE) optimality. This paper proposes a novel denoising strategy…

We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…

Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…

Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…

In this paper, we propose a method for denoising diffusion-weighted images (DWI) of the brain using a convolutional neural network trained on realistic, synthetic MR data. We compare our results to averaging of repeated scans, a widespread…

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently,…

Diffusion models are mainly studied on image data. However, non-image data (e.g., tabular data) are also prevalent in real applications and tend to be noisy due to some inevitable factors in the stage of data collection, degrading the…

Uncertainty evaluation is critical in scientific and engineering inverse problems. However, existing benchmarks on Diffusion Inverse Solvers (DIS) primarily focus on reconstruction accuracy but overlook uncertainty and distributional…

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…

Iterative generative models, such as noise conditional score networks and denoising diffusion probabilistic models, produce high quality samples by gradually denoising an initial noise vector. However, their denoising process has many…

Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

We investigate the generalisation performance of Distributed Gradient Descent with Implicit Regularisation and Random Features in the homogenous setting where a network of agents are given data sampled independently from the same unknown…

Denoising Diffusion models have exhibited remarkable capabilities in image generation. However, generating high-quality samples requires a large number of iterations. Knowledge distillation for diffusion models is an effective method to…