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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…
We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a latter time) is…
Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food…
This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…
Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…
Diffusion models have been achieving state-of-the-art results across various generation tasks. However, a notable drawback is their sequential generation process, requiring long-sequence step-by-step generation. Existing methods, such as…
Beam alignment is a key challenge in directional mmWave and THz systems, where narrow beams require accurate yet low-overhead training. Existing learning-based approaches typically predict a single beam and do not quantify uncertainty,…
Humans can effortlessly draw new categories from a single exemplar, a feat that has long posed a challenge for generative models. However, this gap has started to close with recent advances in diffusion models. This one-shot drawing task…
Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…
We propose a zero-shot method for generating images in arbitrary spaces (e.g., a sphere for 360{\deg} panoramas and a mesh surface for texture) using a pretrained image diffusion model. The zero-shot generation of various visual content…
We consider a typical class of systems with delayed nonlinearity, which we show to exhibit chaotic diffusion. It is demonstrated that a periodic modulation of the time-lag can lead to an enhancement of the diffusion constant by several…
Generating high-quality synthetic time series is a fundamental yet challenging task across domains such as forecasting and anomaly detection, where real data can be scarce, noisy, or costly to collect. Unlike static data generation,…
Diffusion models have recently enabled state-of-the-art reconstruction of positron emission tomography (PET) images while requiring only image training data. However, domain shift remains a key concern for clinical adoption: priors trained…
Diffusion-based image generators are promising priors for ill-posed inverse problems like sparse-view X-ray Computed Tomography (CT). As most studies consider synthetic data, it is not clear whether training data mismatch (``domain shift'')…
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
Though Transformers have achieved promising results in many computer vision tasks, they tend to be over-confident in predictions, as the standard Dot Product Self-Attention (DPSA) can barely preserve distance for the unbounded input domain.…
Masked diffusion models (MDMs) have achieved notable progress in modeling discrete data, while their potential in molecular generation remains underexplored. In this work, we explore their potential and introduce the surprising result that…
In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…
Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…