Statistical Bias and Effective Dynamics of JKO Schemes with Estimated Ground Geometry

Can smaller time steps remove errors caused by estimating a transport geometry from finite data? In smooth finite-dimensional local models, optimal-plan response contributes to a bias that can survive exact solves and vanishing steps. A candidate-dependent frozen-plan comparison isolates its endpoint coefficient; the local transport tensor determines its velocity limit. A two-support example proves nonvanishing at fixed entropic regularization. Under independent refreshment, finite-horizon averaging separates drift, fluctuations, and numerical error. In a five-support test, the independently computed coefficient predicts endpoint contrasts within $1.12\%$ and probability-mass contrasts within $1.97\%$ at the smallest perturbation. Plan response partially cancels the frozen response. Split-sample correction reduces leading coordinate-mean bias; on two frozen-feature tasks it improves finite-bank reference tracking by $7.3$–$24.7\%$ while worsening prediction. Flow selection, accurate solution, and predictive quality are distinct objectives.