Establish correctness and optimality of the diagonal Gaussian policy surrogate

Establish whether the diagonal Gaussian trajectory-vector surrogate used by TR-GRPO provides correct likelihoods, calibrated uncertainty, or an optimal approximation to the underlying flow-based trajectory generator.

Background

TR-GRPO uses a diagonal Gaussian over controller-facing trajectory vectors because the flow generator does not expose a directly usable exact density. The paper characterizes this Gaussian as a local differentiable optimization interface rather than the exact likelihood of the underlying flow model.

The surrogate ignores temporal and coordinate correlations as well as multimodality among distinct path families. Although the complete intervention improves contact metrics, the authors explicitly state that the existing evidence does not establish density correctness, calibrated uncertainty, or optimality of the diagonal family.