We present TRACE-GS, an on-policy trajectory distillation framework that leverages privileged geometric conditioning at training time, thereby adapting a diffusion prior to sparse-view 3D Gaussian Splatting (3DGS) restoration. Rather than pursuing increasingly sophisticated restoration architectures, we identify a more fundamental limitation shared by existing diffusion-based approaches: supervision at independently noised states does not cover those reached during inference.

In sparse-view 3DGS, under-constrained geometry biases denoising from the outset, and the resulting deviations compound along the rollout. TRACE-GS instead performs on-policy trajectory distillation: a teacher conditioned on richer geometry from additional training views supplies targets along the sparse-view student's own rollout, aligning denoising directions and cross-view responses at each visited state.

This training-only geometry places TRACE-GS in the learning using privileged information (LUPI) setting. At deployment, only the sparse-view student is retained, and its restored renderings serve as pseudo-observations for 3DGS refinement.

To the best of our knowledge, TRACE-GS is the first to derive on-policy supervision from privileged geometry for sparse-view 3DGS restoration, achieving consistent gains and strong generalization across datasets and sparse-view settings.