Related papers: Diffusion-limited aggregation with jumps and fligh…
Generating visual layouts is an essential ingredient of graphic design. The ability to condition layout generation on a partial subset of component attributes is critical to real-world applications that involve user interaction. Recently,…
Machine learning models struggle with generalization when encountering out-of-distribution (OOD) samples with unexpected distribution shifts. For vision tasks, recent studies have shown that test-time adaptation employing diffusion models…
Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
Typically, aggregation-diffusion is modeled by parabolic equations that combine linear or nonlinear diffusion with a Fokker-Planck convection term. Under very general suitable assumptions, we prove that radial solutions of the evolution…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…
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 emerged as powerful generative models in the text-to-image domain. This paper studies their application as observation-to-action models for imitating human behaviour in sequential environments. Human behaviour is…
We show, in this report, how a population balance model differential equation describing batch crystal growth from solution can be solved in closed form for the case of diffusion limited growth with and without modeling the effects of…
Recent advances in diffusion models have significantly improved the synthesis of materials, textures, and 3D shapes. By conditioning these models via text or images, users can guide the generation, reducing the time required to create…
We consider diffusion-limited annihilating systems with mobile $A$-particles and stationary $B$-particles placed throughout a graph. Mutual annihilation occurs whenever an $A$-particle meets a $B$-particle. Such systems, when ran in…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources…
Vision-Language-Action (VLA) models adapt large vision-language backbones to map images and instructions into robot actions. However, prevailing VLAs either generate actions auto-regressively in a fixed left-to-right order or attach…
Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…
We study the scaling limits of three different aggregation models on the integer lattice Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform…
This paper explores the challenges and benefits of a trainable destruction process in diffusion samplers -- diffusion-based generative models trained to sample an unnormalised density without access to data samples. Contrary to the majority…
Controllable layout generation refers to the process of creating a plausible visual arrangement of elements within a graphic design (e.g., document and web designs) with constraints representing design intentions. Although recent…