6 papers
Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functions
Richard Duong, Viktor Stein, Robert Beinert +2
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals towards given target mea…
Adapting Noise to Data: Generative Flows from 1D Processes
Jannis Chemseddine, Gregor Kornhardt, Richard Duong +1
The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for lea…
Telegrapher's Generative Model via Kac Flows
Richard Duong, Jannis Chemseddine, Peter K. Friz +1
We break the mold in flow-based generative modeling by proposing a new model based on the damped wave equation, also known as telegrapher's equation. Similar to the diffusion equat…
Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once
Moritz Piening, Richard Duong, Gabriele Steidl
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this…
Wasserstein Gradient Flows of MMD Functionals with Distance Kernels under Sobolev Regularization
Richard Duong, Nicolaj Rux, Viktor Stein +1
We consider Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals for positive and negative distance kernels an…
Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometry
Jannis Chemseddine, Christian Wald, Richard Duong +1
We deal with the task of sampling from an unnormalized Boltzmann density by learning a Boltzmann curve given by energies starting in a simple density . First, we…