What Should Few-Step Diffusion Schedules Optimize? Feature-Aligned Timestep Refinement Beyond Numerical Error

Few-step diffusion sampling is highly sensitive to timestep placement, yet existing scheduling objectives are typically derived from numerical or trajectory-level accuracy, while generation quality is evaluated in a nonlinear feature space. We show that this mismatch produces markedly different optimization geometry in the extreme few-step regime: schedules with similar state-space error can have very different Fr\'echet Inception Distance (FID), whereas the feature-mean discrepancy to a high-accuracy reference closely follows the local FID landscape. We therefore use this reference feature-mean discrepancy, the mean component of the FID to the reference, as a local schedule-refinement objective. Rather than assuming global equivalence to data FID, we characterize when its gradient follows the data-mean component and when decreasing that component also decreases FID. We further show that the naive finite-sample plug-in estimator reintroduces a paired feature-dispersion term and derive an unbiased $U$-statistic estimator. The resulting method requires neither model retraining nor real-data statistics during schedule search. Across eight pixel-space settings spanning three datasets, four solvers, and 4–16 function evaluations (NFE), our schedules lie $0.47$–$4.13\%$ above best-found direct-FID solutions (median $1.78\%$), versus median gaps of $16.48\%$ for paired feature error and $59.8\%$ for state-space error. The same objective also transfers to LD3's richer two-sequence parameterization, improving its released schedule from FID $9.632$ to $8.093$ at 4 NFE and from $2.369$ to $2.201$ at 10 NFE.