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Recent advances in latent diffusion models have demonstrated state-of-the-art performance in high-dimensional time-series data synthesis while providing flexible control through conditioning and guidance. However, existing methodologies…

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…

Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…

Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…

Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic…

Diffusion models rely on a high-dimensional latent space of initial noise seeds, yet it remains unclear whether this space contains sufficient structure to predict properties of the generated samples, such as their classes. In this work, we…

Modern foundation models exhibit remarkable out-of-distribution (OOD) generalization, solving tasks far beyond the support of their training data. However, the theoretical principles underpinning this phenomenon remain elusive. This paper…

We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this…

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically…

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

Diffusion models are powerful generative models that produce high-quality samples from complex data. While their infinite-data behavior is well understood, their generalization with finite data remains less clear. Classical learning theory…

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…

The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…

Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…

Diffusion models are a class of generative models that serve to establish a stochastic transport map between an empirically observed, yet unknown, target distribution and a known prior. Despite their remarkable success in real-world…

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…