Related papers: Exact solution of diffusion limited aggregation in…

While diffusion Multimodal Large Language Models (dMLLMs) have recently achieved remarkable strides in multimodal generation, the development of interpretability mechanisms has lagged behind their architectural evolution. Unlike traditional…

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…

Diffusion language models (DLMs) provide a bidirectional generation framework naturally suited for infilling, yet their performance is constrained by the pre-specified infilling length. In this paper, we reveal that DLMs possess an inherent…

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…

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…

With the increasing use of ultrashort laser pulses and nanoscale-materials, one is regularly confronted to situations in which the properties of the media supporting propagation are not varying slowly with time (or space). Hence, the usual…

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…

Denoising diffusion models (DDMs) offer a promising generative approach for combinatorial optimization, yet they often lack the robust exploration capabilities of traditional metaheuristics like evolutionary algorithms (EAs). We propose a…

We study one-dimensional multi-particle Diffusion Limited Aggregation (MDLA) at its critical density $\lambda=1$. Previous works have verified that the size of the aggregate $X_t$ at time $t$ is $t^{1/2}$ in the subcritical regime and…

I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys.…

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…

We performed extensive numerical simulation of diffusion-limited aggregation in two dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D = 1.712 +- 0.002 and its leading correction to scaling are the…

We present a latent diffusion-based differentiable inversion method (LD-DIM) for PDE-constrained inverse problems involving high-dimensional spatially distributed coefficients. LD-DIM couples a pretrained latent diffusion prior with an…

The growth of a diffusion limited aggregation (DLA) cluster with mass $M$ and radius of gyration $R$ is described by a set of growth probabilities $\{ p_i\}$, where $p_i$ is the probability that the perimeter site $i$ will be the next to…

In this work we study the degenerate diffusion equation $\partial_{t}=x^{\alpha}a\left(x\right)\partial_{x}^{2}+b\left(x\right)\partial_{x}$ for $\left(x,t\right)\in\left(0,\infty\right)^{2}$, equipped with a Cauchy initial data and the…

We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…

We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…

Data scarcity is a fundamental barrier in Electrical Impedance Tomography (EIT), as undersampled Dirichlet-to-Neumann (DtN) measurements can substantially degrade conductivity reconstructions. We address this bottleneck by completing…

The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…

Large language models have achieved remarkable success under the autoregressive paradigm, yet high-quality text generation need not be tied to a fixed left-to-right order. Existing alternatives still struggle to jointly achieve generation…