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A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
Diffusion Models have become a cornerstone of modern generative AI for their exceptional generation quality and controllability. However, their inherent \textit{multi-step iterations} and \textit{complex backbone networks} lead to…
Diffusion-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of…
Diffusion models, such as diffusion policy, have achieved state-of-the-art results in robotic manipulation by imitating expert demonstrations. While diffusion models were originally developed for vision tasks like image and video…
Our work focuses on addressing sample deficiency from low-density regions of data manifold in common image datasets. We leverage diffusion process based generative models to synthesize novel images from low-density regions. We observe that…
Model collapse, the severe degradation of generative models when iteratively trained on their own outputs, has gained significant attention in recent years. This paper examines Chain of Diffusion, where a pretrained text-to-image diffusion…
In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In…
Humans excel at discovering regular structures from limited samples and applying inferred rules to novel settings. We investigate whether modern generative models can similarly learn underlying rules from finite samples and perform…
With the rise of generative models, there is a growing interest in unifying all tasks within a generative framework. Anomaly detection methods also fall into this scope and utilize diffusion models to generate or reconstruct normal samples…
Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
Generative models, such as GANs and diffusion models, have been used to augment training sets and boost performances in different tasks. We focus on generative models for cell detection instead, i.e., locating and classifying cells in given…
We study the iterated Galton-Watson process (IGW), possibly with thinning, introduced by Gawe{\l}and Kimmel to model the number of repeats of DNA triplets during some genetic disorders. If the process involves some thinning, then extinction…
Reinforced Galton-Watson processes have been introduced in arxiv:2306.02476 as population models with non-overlapping generations, such that reproduction events along genealogical lines can be repeated at random. We investigate here some of…
Diffusion models exhibit impressive generative capabilities but are significantly impacted by exposure bias. In this paper, we make a key observation: the energy of predicted noisy samples in the reverse process continuously declines…
Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…
Diffusion models have become a mainstream approach for high-resolution image synthesis. However, directly generating higher-resolution images from pretrained diffusion models will encounter unreasonable object duplication and exponentially…
Data-driven generative models excel in language and vision, but diffusion models often fail in constrained planning and design tasks, exhibiting severe constraint violations in engineering inverse design, molecular generation, multi-robot…