One-Step Generative Modeling via Training Dynamics Action

Zhangyong Liang, Ying Huang, Haibin Ling

One-step generative models construct a static generator through iterative training-time transport. Existing transport objectives primarily assess distributional motion, although a neural generator needs to realize the requested sample displacements jointly through shared parameter updates. The training-time construction raises the question: \emph{once training becomes the iterative process that constructs the final one-step map, what to optimize: the next distributional move, or the route by which the finite generator learns the final map?} To address the question, we introduce \textbf{T}raining \textbf{D}ynamics \textbf{A}ction (\textbf{TDAction}), which selects transport targets according to local shared-parameter realization cost while retaining a prescribed level of distributional progress. We formulate the cost as a soft-terminal control problem and derive a closed-form Batch Tangent Action-to-Go value that accounts for parameter effort and terminal mismatch. The criterion captures cross-sample interactions omitted by independent pairwise costs; under isotropic mobility, the criterion agrees with quadratic Euclidean assignment for deterministic balanced couplings. Randomized…