6 papers · 1 filter
Statistical Convergence of Spherical First Hitting Diffusion Models
Simon Bienewald, Lukas Trottner
Denoising diffusion models have evolved into a state-of-the-art method for tasks in various fields, such as denoising and generation of images, text generation, or generation of sy…
Reflected diffusion models adapt to low-dimensional data
Asbjørn Holk, Claudia Strauch, Lukas Trottner
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data re…
Statistical guarantees for denoising reflected diffusion models
Asbjørn Holk, Claudia Strauch, Lukas Trottner
In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical…
Model-free filtering in high dimensions via projection and score-based diffusions
Sören Christensen, Jan Kallsen, Claudia Strauch +1
We consider the problem of recovering a latent signal from its noisy observation . The unknown law of , and in particular its support , are ac…
Multivariate change estimation for a stochastic heat equation from local measurements
Anton Tiepner, Lukas Trottner
We study a stochastic heat equation with piecewise constant diffusivity having a jump at a hypersurface that splits the underlying space , into two dis…
Change point estimation for a stochastic heat equation
Markus ReiÃ, Claudia Strauch, Lukas Trottner
We study a change point model based on a stochastic partial differential equation (SPDE) corresponding to the heat equation governed by the weighted Laplacian $Î_\vartheta = \nabl…