Related papers: Directed Diffusion-Limited Aggregation
Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the…
Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models,…
Improving the understanding of diffusive processes in networks with complex topologies is one of the main challenges of today's complexity science. Each network possesses an intrinsic diffusive potential that depends on its structural…
We consider the finite volume approximation of a reaction-diffusion system with fast reversible reaction. We deduce from a priori estimates that the approximate solution converges to the weak solution of the reaction-diffusion problem and…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…
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.…
One of the most compelling features of global discrete diffusion language models is their global bidirectional contextual capability. However, existing block-based diffusion studies tend to introduce autoregressive priors, which, while…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
An implicit Euler finite-volume scheme for general cross-diffusion systems with volume-filling constraints is proposed and analyzed. The diffusion matrix may be nonsymmetric and not positive semidefinite, but the diffusion system is assumed…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
Diffusion-based models have gained significant popularity for text-to-image generation due to their exceptional image-generation capabilities. A risk with these models is the potential generation of inappropriate content, such as biased or…
The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are…
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…
We consider a family of controlled reaction-diffusion equations, describing the spatial spreading of an invasive biological species. For a given propagation speed $c\in{I\!\!R}$, we seek a control with minimum cost, which achieves a…
Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a…