Related papers: Saffman-Taylor Fingers at Intermediate Noise
This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…
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…
In the nonlinear diffusion framework, stochastic processes of McKean-Vlasov type play an important role. In some cases they correspond to processes attracted by their own probability distribution: the so-called self-stabilizing processes.…
Classical diffusion models typically rely on isotropic Gaussian noise, treating all regions uniformly and overlooking structural information important for high-quality generation. We introduce an edge-preserving diffusion process that…
Decentralized learning and optimization is a central problem in control that encompasses several existing and emerging applications, such as federated learning. While there exists a vast literature on this topic and most methods centered…
Transformer architecture has been very successful long runner in the field of Deep Learning (DL) and Large Language Models (LLM) because of its powerful attention-based learning and parallel-natured architecture. As the models grow gigantic…
Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that…
Diffusion models have emerged as a robust framework for various generative tasks, including tabular data synthesis. However, current tabular diffusion models tend to inherit bias in the training dataset and generate biased synthetic data,…
DIFF Transformer improves attention allocation by enhancing focus on relevant context while suppressing noise. It introduces a differential attention mechanism that calculates the difference between two independently generated attention…
Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
Video editing and generation methods often rely on pre-trained image-based diffusion models. During the diffusion process, however, the reliance on rudimentary noise sampling techniques that do not preserve correlations present in…
Supervised Gaussian denoisers exhibit limited generalization when confronted with out-of-distribution noise, due to the diverse distributional characteristics of different noise types. To bridge this gap, we propose a histogram matching…
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
We discuss the quantization of sound waves in a fluid with a linear dispersion relation and calculate the quantum density fluctuations of the fluid in several cases. These include a fluid in its ground state. In this case, we discuss the…
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…
The advent of open-source AI communities has produced a cornucopia of powerful text-guided diffusion models that are trained on various datasets. While few explorations have been conducted on ensembling such models to combine their…
Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…