Related papers: Improved Sample Complexity Bounds for Diffusion Mo…
Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…
Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…
Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models…
Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both…
Diffusion models are one of the most important families of deep generative models. In this note, we derive a quantitative upper bound on the Wasserstein distance between the data-generating distribution and the distribution learned by a…
This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…
Diffusion models have attained prominence for their ability to synthesize a probability distribution for a given dataset via a diffusion process, enabling the generation of new data points with high fidelity. However, diffusion processes…
Used as priors for Bayesian inverse problems, diffusion models have recently attracted considerable attention in the literature. Their flexibility and high variance enable them to generate multiple solutions for a given task, such as…
Group-invariant probability distributions appear in many data-generative models in machine learning, such as graphs, point clouds, and images. In practice, one often needs to estimate divergences between such distributions. In this work, we…
Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…
Channel modelling is essential to designing modern wireless communication systems. The increasing complexity of channel modelling and the cost of collecting high-quality wireless channel data have become major challenges. In this paper, we…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
As a highly expressive generative model, diffusion models have demonstrated exceptional success across various domains, including image generation, natural language processing, and combinatorial optimization. However, as data distributions…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…