PRISM: Probabilistic 3D Restoration via Inter-band Spectral Modeling

Real-world 3D point clouds are often affected by mixed corruptions, including noise, occlusion, and background interference. Existing methods generally lack explicit physical modeling of corruption, making it difficult to distinguish stochastic disturbances from true geometry or use object-level geometric context to constrain local completion. We therefore reformulate restoration as a “physics-aware spectral generation” problem. Using a fixed 3D discrete wavelet transform, we analyze the frequency-band responses of four corruption operators, express observation changes as operator-induced coefficient deviations, and characterize band-wise differences between stochastic disturbances and true geometry, as well as cross-band relations between the low-frequency skeleton and high-frequency details induced by structural degradation. Building on this analysis, we propose PRISM (Probabilistic 3D Restoration via Inter-band Spectral Modeling), a physics-aware wavelet-based generative framework. Following the Knothe-Rosenblatt (KR) rearrangement theorem, we design an Inter-band Dual-Stream Probabilistic Bridge that decomposes complex joint-distribution inference into cascaded inference of the marginal distribution of the low-frequency skeleton and the conditional distribution of high-frequency details. Experiments show that PRISM provides a physically interpretable inference path and significantly outperforms existing methods on challenging mixed-corruption benchmarks. Code will be released soon.