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About this paper
Maria Oprea, Qin Li, Yunan Yang
A Wasserstein-space analogue of stochastic-gradient diffusion matching is developed by replacing sample-dependent velocity fields with Gaussian random fields having identical conditional means and covariances. For sufficiently regular observables, the resulting discrete-time schemes differ by global weak error O(h²) over a fixed time horizon, with numerical tests confirming the predicted rate and showing that third moments determine the leading residual error.
Key insights
- Conditional mean and covariance of the stochastic velocity determine the dynamics through second weak order; non-Gaussian features first appear through third and higher moments.
- The Gaussian surrogate is state-dependent, with its mean and covariance recomputed from the current probability measure rather than fixed in advance.
- The analysis compares expectations of regular test functionals, not the random measures directly, and relies on compact-domain, moment, and stability assumptions.
Summary by alphaXiv.
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