arXiv research

Classifies solitons for surface diffusion flow of graphs.

Surface diffusion and mean curvature flows converge to stable critical sets in flat tori.

Paper proves inequality for curves, applies to surface diffusion flow.

Analyzed geometric and diffusion properties of a coupled system.

We consider closed immersed hypersurfaces in $\R^3$ and $\R^4$ evolving by a special class of constrained surface diffusion flows. This class of constrained flows includes the classical surface diffusion flow. In this paper we present a Lifespan Theorem for these flows, which gives a positive lower bound on the time fo…

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total cur…

In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, tr…

We prove the sharp local L^1 - L^\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\infty estimate for p larger than 1. It also has several applications in geometry, providing …

We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly immersed stationary (ΔH \equiv 0) hypersurface in \R^3 or \R^4 with restricted growth of the curvature at infinity and small total tracefree c…

Self-similar solutions to geometric flows are stable under small perturbations.

Existence of translating solutions shown for curve diffusion flow.

It is the purpose of this article to establish a technical tool to study regularity of solutions to parabolic equations on manifolds. As applications of this technique, we prove that solutions to the Ricci-DeTurck flow, the surface diffusion flow and the mean curvature flow enjoy joint analyticity in time and space, an…

DYffusion improves diffusion models for spatiotemporal forecasting.

Study shows diffused interface flows to single diffused balls over time.

We show the existence of a global unique and analytic solution for the mean curvature flow, the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with small Lipschitz norm. We also show the existence of a global unique and analytic solution to the Ricci-DeTurck flow on euclidean s…

We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and ap…

Paper introduces new methods for modeling categorical data.

Smooth convergence shown for curve diffusion flows.

This work interprets diffusion score matching using normalizing flows for better model training and evaluations.

Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternati…

New method uses diffusion models to solve inverse problems.

Flow Matching enables robust training of CNFs with various probability paths.

New jellyfish found in various flows.

Efficiently solves inverse problems with diffusion and flow models in just a few steps.

Curves become nearly circular over time without initial assumptions.

GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.

New method identifies drift and diffusivity from SDE marginals.

The study examines how shallow neural nets converge to training samples or manifold points during diffusion.

We present a novel approximate inference method for diffusion processes, based on the Wasserstein gradient flow formulation of the diffusion. In this formulation, the time-dependent density of the diffusion is derived as the limit of implicit Euler steps that follow the gradients of a particular free energy functional.…

Neural Flow Diffusion Models improve diffusion models by learning flexible forward processes.

We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.

New method for estimating diffusion model densities without solving flows.

The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.

New method shortens and straightens curves, proving convergence and well-posedness.

New method learns discrete graph diffusion via free-energy gradient flows.

Improved NPE with conditional diffusions and summary networks.

New diffusion models capture heavy-tailed distributions better.

Bi-Lipschitz flows approximate a wide range of distributions.

Curve diffusion flow straightens curves with endpoints on intersecting lines.

New error bounds for flow matching methods using deterministic sampling.

Novel alignment framework for text-to-image generation using diffusion models and flow matching.

We prove a blow-up criterion in terms of an $L_2$-bound of the curvature for solutions to the curve diffusion flow if the maximal time of existence is finite. In our setting, we consider an evolving family of curves driven by curve diffusion flow, which has free boundary points supported on a line. The evolving curve h…

Language Rectified Flow improves diffusion language generation by simplifying complex steps.

Generative models tackle incompressible fluid flows by enforcing divergence-free constraints.

LFM learns a sequence of smaller models to generate data from noise.

Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.

Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.

The paper improves the probability flow ODE sampler for faster sampling of natural images.