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The properties of the fluctuations large enough to induce bifurcations at open chemical systems at steady constraints are studied. The fluctuations that come from the diffusion-induced noise are considered. It is a generic for the surface…

Diffusion models have shown great results in image generation and in image editing. However, current approaches are limited to low resolutions due to the computational cost of training diffusion models for high-resolution generation. We…

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics…

Despite recent advances in large-scale text-to-image generative models, manipulating real images with these models remains a challenging problem. The main limitations of existing editing methods are that they either fail to perform with…

This study addresses the challenge of, without training or fine-tuning, controlling the global color aspect of images generated with a diffusion model. We rewrite the guidance equations to ensure that the outputs are closer to a known color…

The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…

This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…

This work develops a robust diffusion recursive least squares algorithm to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. This algorithm minimizes an exponentially weighted…

Diffusion models generate high-resolution images through iterative stochastic processes. In particular, the denoising method is one of the most popular approaches that predicts the noise in samples and denoises it at each time step. It has…

We control the diffusion of light in a disordered photonic waveguide by modulating the waveguide geometry. In a single waveguide of varying cross-section, the diffusion coefficient changes spatially in two dimensions due to localization…

A model of noise reduction (NR) for signal processing is introduced. Each noise source puts a symmetric constraint on the space of the signal vector within a tolerable overlap. When the number of noise sources increases, sequences of…

Diffusion models generate images with an unprecedented level of quality, but how can we freely rearrange image layouts? Recent works generate controllable scenes via learning spatially disentangled latent codes, but these methods do not…

Image retouching aims to enhance the visual quality of photos. Considering the different aesthetic preferences of users, the target of retouching is subjective. However, current retouching methods mostly adopt deterministic models, which…

Recently, it has been shown that investing computing resources in searching for good initial noise for a text-to-image diffusion model helps improve performance. However, previous studies required external models to evaluate the resulting…

We present ControlNet, a neural network architecture to add spatial conditioning controls to large, pretrained text-to-image diffusion models. ControlNet locks the production-ready large diffusion models, and reuses their deep and robust…

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term…

While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances…

Diffusion models have revolutionized image generation and editing, producing state-of-the-art results in conditioned and unconditioned image synthesis. While current techniques enable user control over the degree of change in an image edit,…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this…