Related papers: Degenerate diffusions arising from gene duplicatio…
This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We present a detailed kinetic model for the Polymerase Chain Reaction, and model the probability of replication in terms of the physical parameters of the problem. Applying the theory of branching processes, we show the existance of a new…
We present a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions. Key steps are understanding how these models interrelate when the ultra-violet cut-off strategy is…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
Diffusion models have achieved remarkable progress in generative modelling, particularly in enhancing image quality to conform to human preferences. Recently, these models have also been applied to low-level computer vision for…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
We consider a quasilinear degenerate diffusion-reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity…
We propose in this paper an analytically new construct of a diffusion model whose drift and diffusion parameters yield an exponentially time-decaying Signal to Noise Ratio in the forward process. In reverse, the construct cleverly carries…
Experiments on carrier recombination in two-dimensional organic structures are often interpreted in the frame of the Langevin model with taking into account only the drift of the charge carriers in their mutual electric field. While this…
As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…
The task of deducing three-dimensional molecular configurations from their two-dimensional graph representations holds paramount importance in the fields of computational chemistry and pharmaceutical development. The rapid advancement of…
Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion…
Machine learning enables unbinned, highly-differential cross section measurements. A recent idea uses generative models to morph a starting simulation into the unfolded data. We show how to extend two morphing techniques, Schr\"odinger…
Detectors often suffer from performance drop due to domain gap between training and testing data. Recent methods explore diffusion models applied to domain generalization (DG) and adaptation (DA) tasks, but still struggle with large…
Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
Generative AI models have revolutionized various fields by enabling the creation of realistic and diverse data samples. Among these models, diffusion models have emerged as a powerful approach for generating high-quality images, text, and…
One-dimensional Fisher-Wright diffusion process on the interval $(0,1)$ with mutations is considered. This is a widely known model in population genetics. The goal of the paper is an exponential recurrence of the process, which also implies…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…