DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting

arXiv:2607.10912v1 Announce Type: new Abstract: 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 -- and, as a theory-backed alternative, 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 makes the per-step cost independent of the number of points. We give an exact monotonicity guarantee, a rigorous truncation-error bound correcting an anti-conservative large-$\alpha$ approximation in common use, and an honest account of what the fitted number of components estimates. Empirically: (i) the effective complexity $\hat{K}$ adapts to scene complexity and recovers the true $K$ within $\pm 1$ on well-separated synthetic data with regime-appropriate concentration; (ii) a deconfounded comparison shows the DP prior's contribution is complexity selection, not per-component efficiency -- converged DP fits exceed single-pass fixed-$K$ VBGS by +2.7 dB at matched budgets yet tie an equally converged fixed-$K$ baseline, and on 3D scenes DP-Splat matches or exceeds VBGS's held-out color prediction with 5.9-7.6x fewer components; (iii) the posterior-predictive color variance is well calibrated on model-matched synthetic data; and (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, a gap between variational practice and posterior asymptotics documented across three orders of magnitude in $N$.