Related papers: Random Growth via Gradient Flow Aggregation
The dynamics of small global perturbations in the form of linear combination of a finite number of non-axisymmetric eigenmodes is studied in two-dimensional approximation. The background flow is assumed to be an axisymmetric perfect fluid…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…
Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a…
Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they…
In unconstrained optimisation on an Euclidean space, to prove convergence in Gradient Descent processes (GD) $x_{n+1}=x_n-\delta _n \nabla f(x_n)$ it usually is required that the learning rates $\delta _n$'s are bounded: $\delta _n\leq…
In the classical model of Diffusion Limited Aggregation (DLA), introduced by Witten and Sander, the process begins with a single particle cluster placed at the origin of a space, and then, one at a time, particles make a random walk from…
Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by…
We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for…
In the present note we analyze the one-dimensional multi-particle diffusion limited aggregation (MDLA) model: the initial number of particles at each positive integer site has Poisson distribution with mean $\mu$, independently of all other…
Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no boundary proposal, specifically the…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
We introduce a novel stochastic growth process, the record-driven growth process, which originates from the analysis of a class of growing networks in a universal limiting regime. Nodes are added one by one to a network, each node…
We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes…
Flow-based generative models enjoy certain advantages in computing the data generation and the likelihood, and have recently shown competitive empirical performance. Compared to the accumulating theoretical studies on related score-based…
A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized…
We study a stochastic Laplacian growth model, where a set $\mathbf{U}\subseteq\mathbb{R}^{\mathrm{d}}$ grows according to a reflecting Brownian motion in $\mathbf{U}$ stopped at level sets of its boundary local time. We derive a scaling…
Stochastic Gradient Descent (SGD) has been the method of choice for learning large-scale non-convex models. While a general analysis of when SGD works has been elusive, there has been a lot of recent progress in understanding the…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
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…