Related papers: McLachlan-projected reduced dynamics for ill-posed…
Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…
We consider semidiscrete finite differences schemes for the periodic Scr\"odinger equation in dimension one. We analyze whether the space-time integrability properties observed by Bourgain in the continuous case are satisfied at the…
Diffusion-based language models (dLLMs) have emerged as a promising alternative to autoregressive language models, offering the potential for parallel token generation and bidirectional context modeling. However, harnessing this flexibility…
We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. While image editing with GANs builds upon latent space, DMs rely on editing the conditions such as text prompts. We present an…
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two…
Masked diffusion language models (MDLMs) generate text via iterative masked-token denoising, enabling mask-parallel decoding and distinct controllability and efficiency tradeoffs from autoregressive LLMs. Yet, efficient representation-level…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Standard diffusion corrupts data using Gaussian noise whose Fourier coefficients have random magnitudes and random phases. While effective for unconditional or text-to-image generation, corrupting phase components destroys spatial…
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the…
We show that deliberately breaking detailed balance in generative diffusion processes can accelerate the reverse process without changing the stationary distribution. Considering the Ornstein--Uhlenbeck process, we decompose the dynamics…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
Snapshot compressive spectral imaging reconstruction aims to reconstruct three-dimensional spatial-spectral images from a single-shot two-dimensional compressed measurement. Existing state-of-the-art methods are mostly based on deep…
Let G \subset \R^k be a convex polyhedral cone with vertex at the origin given as the intersection of half spaces {G_i, i= 1, ..., N}, where n_i and d_i denote the inward normal and direction of constraint associated with G_i, respectively.…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
Spatial profiling technologies in biology, such as imaging mass cytometry (IMC) and spatial transcriptomics (ST), generate high-dimensional, multi-channel data with strong spatial alignment and complex inter-channel relationships.…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed…