Stability-Guided Relative Geometry Distillation via Interpolated Pseudo-Views for Sparse-View 3D Gaussian Splatting

Extremely sparse-view 3D Gaussian Splatting (3DGS) often suffers from depth drift, incorrect occlusions, and floating artifacts because supervision is unavailable between training cameras. We propose a stability-guided relative geometry distillation (SG-RGD) framework that extends geometric supervision to interpolated pseudo-views while reducing the influence of unreliable regions. Perturbation-based Pseudo-view Stability (PVS) estimates pixel-wise continuous stability weights from appearance differences between normal and mildly scale-perturbed renderings at the same pseudo-camera. Relative geometry distillation (RGD) uses these weights to modulate scale- and shift-invariant correlation alignment between Gaussian-rendered depth and relative depth predicted by a frozen monocular teacher. Progressive Multi-scale Pseudo-depth Curriculum (PMPC) introduces this supervision in a coarse-to-fine manner. On the nine-scene Mip-NeRF 360 three-view benchmark, SG-RGD improves PSNR from 10.6955 to 10.9600 dB and SSIM from 0.1422 to 0.2150 while reducing LPIPS from 0.7146 to 0.7100 and AVGE from 0.3849 to 0.3716 compared with DNGaussian. Experiments on Mip-NeRF 360 six-view and NeRF Synthetic eight-view further characterize performance across view coverage and data distributions, while ground-truth geometry diagnostics show that lower stability weights tend to correspond to larger geometric errors. All proposed modules are training only, preserving the standard 3DGS inference pipeline.