Establishes a unified temporal-spatial minimax lower bound of order M to the power of minus gamma_d times (k+1) over (k+1 plus gamma_d) for W2-risk of future distribution estimates under k-th order adiabatic smoothness on the velocity field.
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3 Pith papers cite this work. Polarity classification is still indexing.
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Two-parameter flows learn base-to-marginal transports via conditional flow matching then extract unique physics-time velocities by regression on synthetic trajectories, inheriting regularity and scaling to high dimensions while permitting non-gradient dynamics.
Presents a drift transformation framework for multidimensional diffusions that yields product-form transition densities, with explicit results for Wiener and Ornstein-Uhlenbeck cases including resetting and stochastic ordering.
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A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
Establishes a unified temporal-spatial minimax lower bound of order M to the power of minus gamma_d times (k+1) over (k+1 plus gamma_d) for W2-risk of future distribution estimates under k-th order adiabatic smoothness on the velocity field.