Eulerian Gaussian Splatting using Hashed Probability Pyramids

2026-05-27

AI Summary

This work addresses the limitations of conventional 3D Gaussian Splatting, which relies on heuristic primitive manipulations—such as manually tuned densification strategies—that hinder stable optimization and impede natural exploration of volumetric structure. The authors propose a probabilistic density field–based Gaussian Splatting framework, where Gaussian positions are treated as samples drawn from a learnable volumetric density field. By leveraging a multi-scale hash grid, the method enables end-to-end gradient-based optimization without heuristic interventions. Unbiased gradient estimation and control variates are introduced to reduce variance, allowing probability mass to flow adaptively according to the loss landscape without fragile priors. Experiments demonstrate that the approach achieves state-of-the-art reconstruction quality on the mip-NeRF 360 benchmark while maintaining real-time rendering speeds comparable to the original 3DGS.

Abstract

We introduce a probabilistic splat-based radiance field framework that retains the fast rasterization and test-time efficiency of 3D Gaussian Splatting (3DGS) while replacing heuristic primitive manipulation with gradient-based optimization of a volumetric probability density. Rather than relocating, splitting, or culling Gaussians via hand-tuned densification (e.g., ADC), we treat primitive locations as samples drawn from a persistent, learnable density. We instantiate this density using a novel, memory-efficient multi-scale hierarchical grid that enables end-to-end gradient-based optimization. To stabilize the optimization, we derive an unbiased gradient estimator with control variates that markedly reduces variance. By allowing probability mass to flow to where the loss demands, our framework eliminates brittle priors and naturally explores the volume, achieving state-of-the-art reconstruction quality on mip-NeRF 360 while preserving 3DGS-level rendering speed.

Problem

• 3D Gaussian Splatting
• radiance field
• gradient-based optimization
• volumetric probability density
• reconstruction quality

Innovation

• Eulerian Gaussian Splatting
• probabilistic radiance fields
• gradient-based optimization
• hashed probability pyramids
• unbiased gradient estimator