Coupled Subsets for Self-Supervised Point Cloud Denoising from a Single Scan

Noisy-only learning allows point cloud denoisers to be trained without clean targets. When only a single scan of each shape is available, a natural way to obtain Noise2Noise-style supervision is to split the scan into two subsets and enforce consistency between their denoised outputs. This strategy, however, implicitly assumes that the two subsets share the same clean samples. We observe that this assumption generally fails for point clouds: subsets drawn from one scan contain different surface samples that differ in spatial coverage and local density. We term this discrepancy the coupling gap and show that a set-level consistency loss cannot be reduced below it without moving the outputs away from the clean geometry. We address the coupling gap at two levels. At the data level, a coupled paired-subset sampler builds the subsets from local point pairs, which bounds the coupling gap. At the representation level, an invertible network factorizes the latent space into a subset-invariant structure stream and a subset-specific nuisance stream, and reconstructs denoised coordinates from the structure stream alone; unlike prior factorizations, it is learned without clean targets. Training combines an Earth Mover's Distance between the denoised subsets, an entropic optimal-transport consistency between structure latents, and an input-constrained displacement regularizer. Experiments on synthetic benchmarks and real scans show that our method achieves the best overall performance among noisy-only denoisers and remains competitive with supervised denoisers. Code will be made publicly available.