Related papers: Score-Optimal Diffusion Schedules

The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…

In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in $\mathbb{R}^d$ to within $\varepsilon$ total-variation distance, we…

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…

Sampling from unnormalized target distributions is a fundamental yet challenging task in machine learning and statistics. Existing sampling algorithms typically require many iterative steps to produce high-quality samples, leading to high…

Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique.…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on…

Diffusion models generate samples by iteratively denoising a Gaussian prior, traversing a sequence of noise levels that, in every published sampler, decreases monotonically. Six years of intensive work has refined nearly every aspect of…

Network optimization is a fundamental challenge in the Internet of Things (IoT) network, often characterized by complex features that make it difficult to solve these problems. Recently, generative diffusion models (GDMs) have emerged as a…

Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…

Denoising Diffusion Probabilistic Models (DDPM) have recently gained significant attention. DDPMs compose a Markovian process that begins in the data domain and gradually adds noise until reaching pure white noise. DDPMs generate…

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by…

Diffusion modeling (DM) has high-quality generative performance, and the sampling problem is an important part of the DM performance. Thanks to efficient differential equation solvers, the sampling speed can be reduced while higher sampling…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Generative diffusion models have emerged as leading models in speech and image generation. However, in order to perform well with a small number of denoising steps, a costly tuning of the set of noise parameters is needed. In this work, we…

Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…