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Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…

Recently, motivated by the outstanding achievements of diffusion models, the diffusion process has been employed to strengthen representation learning in recommendation systems. Most diffusion-based recommendation models typically utilize…

Diffusion models generate samples through an iterative denoising process, guided by a neural network. While training the denoiser on real-world data is computationally demanding, the sampling procedure itself is more flexible. This…

Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…

Diffusion models have emerged as powerful tools for high-quality image generation and editing, but guiding these models to produce specific outputs remains a challenge. Conventional approaches rely on conditioning mechanisms, such as text…

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically…

We present an novel framework for efficiently and effectively extending the powerful continuous diffusion processes to discrete modeling. Previous approaches have suffered from the discrepancy between discrete data and continuous modeling.…

Discrete diffusion models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain significantly less understood than those of their…

Can a diffusion model trained on bedrooms recover human faces? Diffusion models are widely used as priors for inverse problems, but standard approaches usually assume a high-fidelity model trained on data that closely match the unknown…

Diffusion probabilistic models have recently achieved remarkable success in generating high-quality images. However, balancing high perceptual quality and low distortion remains challenging in application of diffusion models in image…

A controllable energy method, which considers the undersampling issue of the transfer function and valid spectral energy of a source signal, is proposed to implement angular spectrum diffraction calculation in near and far fields. The…

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

Diffusion models have shown promising results for a wide range of generative tasks with continuous data, such as image and audio synthesis. However, little progress has been made on using diffusion models to generate discrete symbolic music…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training…

We introduce Diffusion Active Learning, a novel approach that combines generative diffusion modeling with data-driven sequential experimental design to adaptively acquire data for inverse problems. Although broadly applicable, we focus on…

Dataset bias is a significant challenge in machine learning, where specific attributes, such as texture or color of the images are unintentionally learned resulting in detrimental performance. To address this, previous efforts have focused…

Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…

Diffusion models have become increasingly popular for generative modeling due to their ability to generate high-quality samples. This has unlocked exciting new possibilities for solving inverse problems, especially in image restoration and…