DP-Splat: Bayesian Nonparametric Complexity Control for Gaussian Splatting

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.