Related papers: Theory of Diffusion Controlled Growth

Diffusion Limited Aggregation and its generalization, Dielectric Breakdown model play an important role in physics, approximating a range of natural phenomena. Yet little is known about them, with the famous Kesten's estimate on the DLAs…

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…

Diffusion models have become popular for policy learning in robotics due to their ability to capture high-dimensional and multimodal distributions. However, diffusion policies are stochastic and typically trained offline, limiting their…

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify…

Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…

Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

Diffusion models have enabled remarkably high-quality medical image generation, yet it is challenging to enforce anatomical constraints in generated images. To this end, we propose a diffusion model-based method that supports…

A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are…

Deep generative models have emerged as promising tools for detecting arbitrary anomalies in data, dispensing with the necessity for manual labelling. Recently, autoregressive transformers have achieved state-of-the-art performance for…

Using recent advances in generative artificial intelligence (AI) brought by diffusion models, this paper introduces a new synergistic method for spectral computed tomography (CT) reconstruction. Diffusion models define a neural network to…

The understanding of magnetic reconnection in three-dimension (3D) is far shallower than its counterpart in two-dimension (2D) due to its potential complication, not to mention the evolving of the spontaneously growing turbulence. We…

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…

We derive a new theoretical interpretation of the reweighted losses that are widely used for training diffusion models. Our method is based on constructing a cascade of time-dependent variational lower bounds on the data log-likelihood,…

Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…

Diffusion models excel at generation, but their latent spaces are high dimensional and not explicitly organized for interpretation or control. We introduce ConDA (Contrastive Diffusion Alignment), a plug-and-play geometry layer that applies…

Diffusion generative models have demonstrated remarkable success in visual domains such as image and video generation. They have also recently emerged as a promising approach in robotics, especially in robot manipulations. Diffusion models…

For real world systems, nonuniform medium is ubiquitous. Therefore, we investigate the diffusion-limited-aggregation process on a two dimensional directed small-world network instead of regular lattice. The network structure is established…

Models of fractal growth commonly consider particles diffusing in a medium and that stick irreversibly to the forming aggregate when making contact for the first time. As shown by the well-known diffusion limited aggregation (DLA) model and…

We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the…