# DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting

arXiv: https://arxiv.org/abs/2607.10912 · HTML: https://mlsanity.com/paper/2607.10912/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 12 Jul 2026.

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [LightGaussian: Unbounded 3D Gaussian Compression with 15x Reduction and 200+ FPS](https://mlsanity.com/paper/2311.17245/) (2023)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [3D Gaussian Splatting as Markov Chain Monte Carlo](https://mlsanity.com/paper/2404.09591/) (2024)
- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [Mixture models with a prior on the number of components](https://mlsanity.com/paper/1502.06241/) (2015)
- [Model-based clustering based on sparse finite Gaussian mixtures](https://mlsanity.com/paper/1606.06828/) (2016)
- [Sparse Variational Student-t Processes](https://mlsanity.com/paper/2312.05568/) (2023)
- [Inconsistency of Pitman-Yor process mixtures for the number of components](https://mlsanity.com/paper/1309.0024/) (2013)
- [Variational Bayes Gaussian Splatting](https://mlsanity.com/paper/2410.03592/) (2024)
- [BOGausS: Better Optimized Gaussian Splatting](https://mlsanity.com/paper/2504.01844/) (2025)
- [Generalized mixtures of finite mixtures and telescoping sampling](https://mlsanity.com/paper/2005.09918/) (2020)
- [Sparse Variational Student-t Processes for Heavy-tailed Modeling](https://mlsanity.com/paper/2408.06699/) (2024)
- [VBGS-SLAM: Variational Bayesian Gaussian Splatting Simultaneous Localization and Mapping](https://mlsanity.com/paper/2604.02696/) (2026)

## Abstract (arXiv)

3D Gaussian Splatting represents scenes as finite mixtures of anisotropic Gaussians whose number of components K is set by heuristic density control or user caps. Variational Bayes Gaussian Splatting (VBGS) recast splat fitting as conjugate variational inference, but K remains fixed. We replace the finite symmetric Dirichlet over mixture weights with a truncated stick-breaking Dirichlet-process prior (or a sparse overfitted finite Dirichlet), so that the number of occupied components adapts to the data while every update remains a closed-form coordinate-ascent step; a natural-gradient stochastic variant scales to large point sets. We give an ELBO monotonicity-and-convergence guarantee, a rigorous truncation-error bound that corrects a large-α approximation in common use which undershoots the exact Ishwaran-James bound, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity hatK adapts to data complexity and recovers the true K within ± 1; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency: converged DP fits beat single-pass fixed-K VBGS by +2.7 dB yet tie an equally converged fixed-K baseline, and on all eight NeRF-synthetic scenes DP-Splat holds held-out point-space color prediction within 0.33 dB of VBGS with 3.9-7.9x fewer occupied components, while under full rasterization on held-out views it renders 3.4-9.0 dB below the unpruned baseline; (iii) the posterior-predictive color variance is well calibrated, and a seeded matched-capacity ablation attributes that calibration to the conjugate color model rather than to the weight prior; (iv) the ordering suggested by exact-posterior asymptotics reverses under mean-field coordinate ascent: the DP prior resists over-splitting while the sparse finite mixture saturates its truncation.