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The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The intra-layer diffusion constants act as small parameter in the expansion and the unperturbed state…

Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network…

Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural…

We use hierarchical procedural rules for the generation of control maps within the stable diffusion framework to produce photo-realistic architectural facade images. Starting from a single input image and its segmentation, we apply an…

Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…

Class-labeled datasets, particularly those common in scientific domains, are rife with internal structure, yet current class-conditional diffusion models ignore these relationships and implicitly diffuse on all classes in a flat fashion. To…

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…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

We present a conditional diffusion model for electromagnetic inverse design that generates structured media geometries directly from target differential scattering cross-section profiles, bypassing expensive iterative optimization. Our 1D…

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are…

In materials science, microstructures and their associated extrinsic properties are critical for engineering advanced structural and functional materials, yet their robust reconstruction and generation remain significant challenges. In this…

Deep generative models dominate the existing literature in layout pattern generation. However, leaving the guarantee of legality to an inexplicable neural network could be problematic in several applications. In this paper, we propose…

Generating realistic sparse multi-category 3D voxel structures is difficult due to the cubic memory scaling of voxel structures and moreover the significant class imbalance caused by sparsity. We introduce Scaffold Diffusion, a generative…

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

Humans naturally obtain intuition about the interactions between and the stability of rigid objects by observing and interacting with the world. It is this intuition that governs the way in which we regularly configure objects in our…

The discovery of inorganic crystal structures with targeted properties is a significant challenge in materials science. Generative models, especially state-of-the-art diffusion models, offer the promise of modeling complex data…

We introduce a framework for automatically defining and learning deep generative models with problem-specific structure. We tackle problem domains that are more traditionally solved by algorithms such as sorting, constraint satisfaction for…

In recent years, diffusion models have become the leading approach for distribution learning. This paper focuses on structure-preserving diffusion models (SPDM), a specific subset of diffusion processes tailored for distributions with…

We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…