# Direct Conditional Parameterization for N-Dimensional Splatting

arXiv: https://arxiv.org/abs/2610.22778 · HTML: https://mlsanity.com/paper/2610.22778/

## Key facts

- No citing papers in the map yet (data through 19 Oct 2026).
- Placed in 3D Gaussian splatting methods, one of 15 directions in 3D reconstruction and neural rendering.
- Builds on 36 of its 40 references that are in the map.
- First posted on arXiv 16 Oct 2026.

## Placed in

- 3D reconstruction and neural rendering / [3D Gaussian splatting methods](https://mlsanity.com/recon3d/3d-gaussian-splatting-methods/)

## Builds on (most cited first, 30 of 36)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields](https://mlsanity.com/paper/2304.06706/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [Language Embedded 3D Gaussians for Open-Vocabulary Scene Understanding](https://mlsanity.com/paper/2311.18482/) (2023)
- [Compact 3D Scene Representation via Self-Organizing Gaussian Grids](https://mlsanity.com/paper/2312.13299/) (2023)
- [Multi-Scale 3D Gaussian Splatting for Anti-Aliased Rendering](https://mlsanity.com/paper/2311.17089/) (2023)
- [GES: Generalized Exponential Splatting for Efficient Radiance Field Rendering](https://mlsanity.com/paper/2402.10128/) (2024)
- [FreeTimeGS: Free Gaussian Primitives at Anytime and Anywhere for Dynamic Scene Reconstruction](https://mlsanity.com/paper/2506.05348/) (2025)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [3D-HGS: 3D Half-Gaussian Splatting](https://mlsanity.com/paper/2406.02720/) (2024)
- [Textured Gaussians for Enhanced 3D Scene Appearance Modeling](https://mlsanity.com/paper/2411.18625/) (2024)
- [Deformable Beta Splatting](https://mlsanity.com/paper/2501.18630/) (2025)
- [Quadratic Gaussian Splatting: High Quality Surface Reconstruction with Second-order Geometric Primitives](https://mlsanity.com/paper/2411.16392/) (2024)
- [7DGS: Unified Spatial-Temporal-Angular Gaussian Splatting](https://mlsanity.com/paper/2503.07946/) (2025)
- [Deformable Radial Kernel Splatting](https://mlsanity.com/paper/2412.11752/) (2024)
- [N-Dimensional Gaussians for Fitting of High Dimensional Functions](https://mlsanity.com/paper/2405.20067/) (2024)
- [6DGS: Enhanced Direction-Aware Gaussian Splatting for Volumetric Rendering](https://mlsanity.com/paper/2410.04974/) (2024)
- [3D Student Splatting and Scooping](https://mlsanity.com/paper/2503.10148/) (2025)

## Abstract (arXiv)

N-dimensional splatting extends 3D Gaussian Splatting with view direction and time to model view-dependent and dynamic effects. Each primitive is lifted into a joint distribution over position and conditioning variables, then conditionally sliced at each rendering query. N-DGS and UBS share this step across Gaussian and Beta kernels: recovering the conditional mean, opacity, and covariance requires per-primitive matrix inversions and regression products in every forward pass. We introduce direct conditional parameterization, replacing this covariance-derived readout with explicit per-effect parameters: a Cholesky precision factor for opacity and a factorized query-to-position regression operator with learnable per-dimension coupling. Unrestricted conditional coordinates recover a valid joint covariance; our factorization adds spatial-scale and coupling priors. Applied to both kernels, the parameterization yields dGS (Gaussian) and dBS (Beta). Across five static and dynamic benchmarks, they match or exceed their covariance-derived counterparts on quality, with gains up to +1.26 dB in the main MCMC evaluation. Production slicing is 6.9-7.7 times faster than on-the-fly covariance-derived conditioning; complete-render profiling gives 1.25-1.91 times speedups on four trained scenes. Direct conditioning provides a structured, kernel-agnostic alternative for N-dimensional splatting. Project page: https://gaozhongpai.github.io/dgs/.