One-Step Generative Modeling via Training Dynamics Action

arXiv:2610.00518v1 Announce Type: new Abstract: 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 tangent probes provide a low-rank implementation that constructs shared detached targets without adding an inference-time trajectory. Controlled studies examine the relationship between generator geometry, transport selection, and realized local action. On ImageNet $256\times256$, TDAction attains an FID below $1.1$ without distillation.

Abstract: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 tangent probes provide a low-rank implementation that constructs shared detached targets without adding an inference-time trajectory. Controlled studies examine the relationship between generator geometry, transport selection, and realized local action. On ImageNet $256\times256$, TDAction attains an FID below $1.1$ without distillation.

Machine Learning (cs.LG)

arXiv:2610.00518 [cs.LG]

(or arXiv:2610.00518v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.00518 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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One-Step Generative Modeling via Training Dynamics Action

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