Latent reasoning models perform multi-step inference in embedding space, reducing the token overhead of chain-of-thought reasoning. Recent training-free refinement methods steer latent trajectories using contrastive signals from stronger and weaker reference checkpoints. We identify three sources of fragility in these methods: hyperparameter sensitivity, reference-pair dependence, and input sensitivity. We propose Trajectory-Invariant Latent Refinement (TILR), a training-free framework that constrains corrections to a stable refinement subspace and adaptively controls their magnitude. First, we extract a spectrally concentrated subspace from strong-weak reference differences across a calibration set and project contrastive updates onto it to filter unstable variation. Second, an adaptive gate scales each update according to its alignment with the learned subspace, suppressing unreliable corrections and recovering the unmodified backbone when alignment is low. Across six reasoning benchmarks, TILR improves robustness to input perturbations and reference selection while maintaining competitive accuracy. On the Coconut backbone, TILR improves answer agreement under semantically equivalent paraphrasing by 11.4% and reduces latent trajectory variance by approximately 30% relative to existing refinement baselines. These results support invariant subspaces as a practical basis for reliable latent refinement without retraining or backpropagation.

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