Consistency-Langevin FastGS: Noise-Tempered Densification to Explain and Improve the Speed–Quality Surprise

TL;DR: Add a tiny bit of smart “wiggle” (noise) to Gaussians where views disagree, so the model finds better placements faster without growing too big. We convert FastGS’s multi-view consistency signal into a stochastic update rule (SGLD-style) and co-regularize it with twin-field disagreement to avoid over-densification. First experiment: on Mip-NeRF 360, compare standard FastGS vs. our noise-tempered variant under the same training budget; hypothesis: same PSNR/LPIPS with fewer Gaussians and faster convergence.

Research Question: Does injecting consistency-weighted stochasticity into Gaussian updates improve optimization stability and let us prune more aggressively, thereby explaining and extending FastGS’s speed-without-quality-loss phenomenon?

Hypothesis: Treating multi-view consistency as a posterior (MCMC view) and adding SGLD-style noise proportional to disagreement will (a) reduce local minima caused by heuristic densification, (b) maintain or improve PSNR/SSIM/LPIPS at equal or lower Gaussian counts, and (c) preserve FastGS’s acceleration while being more robust to poor initializations.

Experiment Plan: - Setup: Implement an SGLD update on Gaussian parameters (position, covariance, opacity, SH) where noise amplitude is tied to two signals: (i) FastGS’s multi-view consistency residual, and (ii) CoR-GS’s twin-field rendering disagreement. Replace heuristic “clone/split” with relocalization moves when uncertainty is high (per 3DGS-as-MCMC).

• Data/Materials: Mip-NeRF 360 and Tanks & Temples scenes; same initialization as Kerbl et al.; same training budget as FastGS.
• Key Measurements: PSNR/SSIM/LPIPS; training wall time; number of Gaussians vs. iteration; failure modes in textureless regions; robustness to degraded SfM initialization.
• Expected Outcomes: SGLD-tempered FastGS matches or exceeds original FastGS quality with fewer Gaussians and equal or better speed; reduced variance across seeds; fewer “floaters” without extra heuristics.

References: ['Ren, S., Wen, T., Fang, Y., & Lu, B. (2025). FastGS: Training 3D Gaussian Splatting in 100 Seconds.', 'Kheradmand, S., Rebain, D., Sharma, G., Sun, W., Tseng, J., Isack, H., Kar, A., Tagliasacchi, A., & Yi, K. M. (2024). 3D Gaussian Splatting as Markov Chain Monte Carlo. Neural Information Processing Systems.', 'Zhang, J., Li, J., Yu, X., Huang, L., Gu, L., Zheng, J., & Bai, X. (2024). CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization. European Conference on Computer Vision.', 'Kerbl, B., Kopanas, G., Leimkuehler, T., & Drettakis, G. (2023). 3D Gaussian Splatting for Real-Time Radiance Field Rendering. ACM Transactions on Graphics.']