3 citations · 15 across the 36 of their papers we have counts for
7 papers · 1 filter
On the Inverse Flow Matching Problem in the One-Dimensional and Gaussian Cases
Alexander Korotin, Gudmund Pammer
This paper studies the inverse problem of flow matching (FM) between distributions with finite exponential moment, a problem motivated by modern generative AI applications such as…
A Brenier Theorem on and Applications to Adapted Transport
Mathias Beiglböck, Gudmund Pammer, Stefan Schrott
We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space and , we construct a full-support probability on $P_2^{N}(H)= P_2(... P_2…
Strassen's theorem for biased convex order
Beatrice Acciaio, Mathias Beiglböck, Evgeny Kolosov +1
Strassen's theorem asserts that for given marginal probabilities there exists a martingale starting in and terminating in if and only if are in convex order. Fr…
Absolutely Continuous Curves of Stochastic Processes
Beatrice Acciaio, Daniel Kršek, Gudmund Pammer +1
We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes…
Estimating causal distances with non-causal ones
Beatrice Acciaio, Songyan Hou, Gudmund Pammer
The adapted Wasserstein () distance refines the classical Wasserstein () distance by incorporating the temporal structure of stochastic processes. This makes the -distan…
The Fundamental Theorem of Weak Optimal Transport
Mathias Beiglböck, Gudmund Pammer, Lorenz Riess +1
The fundamental theorem of classical optimal transport establishes strong duality and characterizes optimizers through a complementary slackness condition. Milestones such as Breni…
The Wasserstein Space of Stochastic Processes in Continuous Time
Daniel Bartl, Mathias Beiglböck, Gudmund Pammer +2
Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the…