相关论文: Concurrence of Symmetry Breaking and Nonlocality P…

With the success of image generation, generative diffusion models are increasingly adopted for discriminative tasks, as pixel generation provides a unified perception interface. However, directly repurposing the generative denoising process…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large…

We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…

Recent advancements in video diffusion models based on Diffusion Transformers (DiTs) have achieved remarkable success in generating temporally coherent videos. Yet, a fundamental question persists: how do these models internally establish…

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…

Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…

Spontaneous symmetry breaking is a hallmark of equilibrium systems, typically characterized by a single critical point separating ordered and disordered phases. Recently, a novel class of non-equilibrium phase transitions was uncovered…

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…

We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow…

Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time…

Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly…

Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power law form for power spectra of temporal fluctuations on all space-time…

Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…

We review recent developments in structural-dynamical phase transitions in trajectory space. An open question is how the dynamic facilitation theory of the glass transition may be reconciled with thermodynamic theories that posit a…

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above…

In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical…

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…

Iterative denoising-based generation, also known as denoising diffusion models, has recently been shown to be comparable in quality to other classes of generative models, and even surpass them. Including, in particular, Generative…