Related papers: Inverting the Ray-Knight identity on the line
Discrete diffusion models have emerged as a promising direction for vision-language tasks, offering bidirectional context modeling and theoretical parallelization. However, their practical application is severely hindered by a…
This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…
Face anonymization aims to protect sensitive identity information by altering faces while preserving visual realism and utility for downstream computer vision tasks. Current methods struggle to simultaneously ensure high image quality,…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…
Deep learning models are known to be vulnerable to adversarial attacks by injecting sophisticated designed perturbations to input data. Training-time defenses still exhibit a significant performance gap between natural accuracy and robust…
Diffusion-based watermarking methods embed verifiable marks by manipulating the initial noise or the reverse diffusion trajectory. However, these methods share a critical assumption: verification can succeed only if the diffusion trajectory…
We prove existence and uniqueness of the reflected backward stochastic differential equation's (RBSDE) solution with a lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous in a filtration…
We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order…
We present a deep learning-based framework for portrait reenactment from a single picture of a target (one-shot) and a video of a driving subject. Existing facial reenactment methods suffer from identity mismatch and produce inconsistent…
An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…
Use denoising diffusion implicit model for bridge-type innovation. The process of adding noise and denoising to an image can be likened to the process of a corpse rotting and a detective restoring the scene of a victim being killed, to help…
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…
This work presents an end-to-end pipeline for generating, refining, and evaluating adversarial patches to compromise facial biometric systems, with applications in forensic analysis and security testing. We utilize FGSM to generate…
Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…
We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each…