Timestep Weighting Through the Lens of Flow Matching Dynamics

Flow matching learns generative models by predicting velocity fields along a predefined path between a prior and a data distribution. The design of the training objective, in particular the weighting across timesteps, is known to have a strong impact on performance, yet further insight into the underlying generation dynamics is needed to guide its design. In this work, we study marginal flow dynamics through the propagation of velocity prediction errors to the generated endpoint. For Gaussian mixture targets, we derive a decomposition of the velocity Jacobian into a within-component term and a term governed by uncertainty over component assignments, and use this structure to approximate timestep-dependent error amplification. We complement the analysis with perturbation probes that measure endpoint sensitivity along model prediction-error directions. Our analysis and observations suggest a transition from an earlier regime in which component ambiguity contributes to error amplification to a later regime in which this contribution diminishes and within-component dynamics dominate. This transition motivates allocating training emphasis asymmetrically across the generation process. Building on logit-normal weighting, we introduce a parameterized refinement that reduces the relative emphasis on the later regime while retaining endpoint suppression. Experiments demonstrate improved generation quality over the logit-normal baseline across multiple image datasets and all tested model sizes.