Related papers: DDPM Score Matching and Distribution Learning
Sequential change-point detection plays a critical role in numerous real-world applications, where timely identification of distributional shifts can greatly mitigate adverse outcomes. Classical methods commonly rely on parametric density…
The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…
We propose the Binary Diffusion Probabilistic Model (BDPM), a generative framework specifically designed for data representations in binary form. Conventional denoising diffusion probabilistic models (DDPMs) assume continuous inputs, use…
Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data,…
Score-based generative models (SGMs) have recently demonstrated impressive results in terms of both sample quality and distribution coverage. However, they are usually applied directly in data space and often require thousands of network…
Denoising Diffusion Probabilistic Models (DDPMs) have significantly advanced generative AI, achieving impressive results in high-quality image and data generation. However, enhancing fidelity without compromising semantic content remains a…
With the incredible results achieved from generative pre-trained transformers (GPT) and diffusion models, generative AI (GenAI) is envisioned to yield remarkable breakthroughs in various industrial and academic domains. In this paper, we…
Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…
We establish minimax convergence rates for score-based generative models (SGMs) under the $1$-Wasserstein distance. Assuming the target density $p^\star$ lies in a nonparametric $\beta$-smooth H\"older class with either compact support or…
This paper provides statistical sample complexity bounds for score-matching and its applications in causal discovery. We demonstrate that accurate estimation of the score function is achievable by training a standard deep ReLU neural…
We introduce the state-of-the-art deep learning Denoising Diffusion Probabilistic Model (DDPM) as a method to infer the volume or number density of giant molecular clouds (GMCs) from projected mass surface density maps. We adopt…
Most existing theoretical investigations of the accuracy of diffusion models, albeit significant, assume the score function has been approximated to a certain accuracy, and then use this a priori bound to control the error of generation.…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…
Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…
We propose a hybrid method for accurately estimating the score function, i.e., the gradient of the log steady-state density, using a Gaussian Mixture Model (GMM) in conjunction with a bisecting K-means clustering step. Our approach, which…
Graph structures offer a versatile framework for representing diverse patterns in nature and complex systems, applicable across domains like molecular chemistry, social networks, and transportation systems. While diffusion models have…
This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion…
Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…