When Motion Accuracy Misleads Downstream Imaging: Evaluating Learned Inverse Models under Slow-Time Near-Equivalence

Learned inverse models often predict an intermediate physical state that a known downstream operator consumes, yet they are commonly trained, validated, and selected by state-space accuracy rather than downstream performance. We ask whether state-space accuracy preserves model ranking for the downstream task when the sampled measurement physics admits approximate equivalences between distant states. We study this in a controlled dynamic Wi-Fi synthetic-aperture simulator: a CNN infers target motion from complex channel-state information and coherent backprojection consumes the inferred velocity. At a 31-Hz diagnostic setting, a state-supervised CNN has lower velocity RMSE than a coherence-regularised CNN (0.149 versus 0.332 m/s) yet higher mean image-localisation error (0.474 versus 0.303 m), in all three training seeds. A sampling-rate diagnostic links the large-error modes to approximate bistatic range-rate branches, and an alias-aware range-rate error agrees better with downstream ranking across the tested estimators, although in a sealed selection experiment it chooses the same model as velocity RMSE. The reversal persists under a fixed update-indexed schedule without validation-based selection, for two architectures (paired image gains of 0.07 and 0.09 m on a sealed 3,000-scene test), under image-grid changes, on a disjoint-support speed holdout, and in an independent ray-traced digital twin for phase-dominated measurements; its size depends on the coherence weight. It weakens or disappears in geometries where few scenes approach the first sampled branch, with more in-distribution training data, at a fixed 100-Hz operating point under the stated speed prior, on a direction holdout, and when deterministic amplitude variation or 0-dB static multipath is present; oracle-motion and static-subtraction controls identify a separate clutter-dominated imaging boundary. These controlled synthetic results support a conditional evaluation principle: when sampled physics admits distant near-equivalent states, Euclidean latent-state accuracy should be reported alongside ambiguity-aware and downstream-task evaluation.