Truncated signature inversion is reframed as learning conditional path distributions via signature-conditioned flow matching, with derived Bayes error baselines and validated reconstruction on real data.
TACache decomposes rectified flow velocity errors into magnitude and direction components to skip steps and reconstruct velocities without extra evaluations, achieving up to 4.14x faster image and 2.11x faster video generation.
Ill-conditioned intermediate covariances make flow matching regress low-variance directions slowly; preconditioning into isotropic space improves optimization and generation quality.
VTV-FM enables second-order flow matching via a minimum-acceleration variational terminal-velocity closure for static data, improving transport geometry and generation quality.
Condition-dependent source distributions for flow matching improve text-to-image generation via variance regularization and directional alignment, accelerating convergence up to 3x in FID.
kFFM replaces arbitrary pairing in Functional Flow Matching with kernel optimal transport to improve infinite-dimensional generative modeling and outperforms baselines on time-series and PDE benchmarks.
RWEFM generatively models meta-distributions on manifolds via Riemannian Wasserstein flow matching, yielding valid flows and efficient GPU-optimal transport approximations for non-Euclidean data.