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Alignment Matters Inside and Out in Equivariant Graph Flow Matching
Moritz Piening, Christian Wald
Graphs are invariant under node permutations, motivating permutation-equivariant architectures in generative models. In flow matching, however, symmetry also affects the source-tar…
Self-Aware Markov Models for Discrete Reasoning
Gregor Kornhardt, Jannis Chemseddine, Christian Wald +1
Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed n…
Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans
Christian Wald, Gabriele Steidl
Among generative neural models, flow matching techniques stand out for their simple applicability and good scaling properties. Here, velocity fields of curves connecting a simple l…
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 e…
Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching
Jannis Chemseddine, Paul Hagemann, Gabriele Steidl +1
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While th…
Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances
Jannis Chemseddine, Paul Hagemann, Christian Wald
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While th…