Related papers: Singularly Perturbed Profiles
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…
Countless systems in biology, physics, and finance undergo diffusive dynamics. Many of these systems, including biomolecules inside cells, active matter systems and foraging animals, exhibit anomalous dynamics where the growth of the mean…
Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…
Personalized diffusion models (PDMs) have become prominent for adapting pre-trained text-to-image models to generate images of specific subjects using minimal training data. However, PDMs are susceptible to minor adversarial perturbations,…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based DDPM models exhibit great potential in generating high-quality…
Magnetic resonance imaging (MRI) is a vital diagnostic tool, but its inherently long acquisition times reduce clinical efficiency and patient comfort. Recent advancements in deep learning, particularly diffusion models, have improved…
A natural desideratum for generative models is self-correction--detecting and revising low-quality tokens at inference. While Masked Diffusion Models (MDMs) have emerged as a promising approach for generative modeling in discrete spaces,…
This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion…
The generation and enhancement of satellite imagery are critical in remote sensing, requiring high-quality, detailed images for accurate analysis. This research introduces a two-stage diffusion model methodology for synthesizing…
The discovery and study of new material systems rely on molecular simulations that often come with significant computational expense. We propose MDDM, a Molecular Dynamics Diffusion Model, which is capable of predicting a valid output…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
Experimental studies of protein-pattern formation have stimulated new interest in the dynamics of reaction-diffusion systems. However, a comprehensive theoretical understanding of the dynamics of such highly nonlinear, spatially extended…
We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…
Diffusion models have opened the path to a wide range of text-based image editing frameworks. However, these typically build on the multi-step nature of the diffusion backwards process, and adapting them to distilled, fast-sampling methods…
Many real-analytic flows, e.g. in chemical kinetics, share a multiple time scale spectral structure. The trajectories of the corresponding dynamical systems are observed to bundle near so-called slow invariant manifolds (SIMs), which are…
Volumetric optical microscopy using non-diffracting beams enables rapid imaging of 3D volumes by projecting them axially to 2D images but lacks crucial depth information. Addressing this, we introduce MicroDiffusion, a pioneering tool…
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…
A central goal in systems biology and drug discovery is to predict the transcriptional response of cells to perturbations. This task is challenging due to the noisy and sparse nature of single-cell measurements, as well as the fact that…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…