Gaussian Flow Dynamics enables simulation-free neural SDEs learning temporal structure
canaesseth · x · 2026-10-06
- The paper (arXiv:2610.04390, Bartosh & Naesseth) shows Gaussian one-time marginals used in simulation-free latent SDE training don't determine dynamics: many processes share the same marginals with different temporal structure, and existing parameterizations fix this implicitly, restricting the posterior family.
- Gaussian flow dynamics construct stochastic processes directly from smoothly evolving Gaussian marginals with explicit, parameterizable gauge degrees of freedom; supports state-dependent diffusion and recovers all linear SDEs with additive noise.
- Gauge Matching combines this with the SDE Matching objective at at-most-quadratic per-step cost, comes within a nat of cubic-cost Helmholtz-SDE on linear benchmarks, matches it on nonlinear systems, and applies where Helmholtz-SDE can't.
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