Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
arXiv:2602. 10099v2 Announce Type: replace Abstract: Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis.
Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space.
arXiv:2607. 05201v1 Announce Type: new Abstract: In non-stationary streaming environments, simultaneously adapting to complex, non-linear domain shifts via continual learning while mitigating the catastrophic effects of severe, uncalibrated label noise poses a fundamental mathematical challenge.
arXiv:2607. 04661v1 Announce Type: cross Abstract: Reconstructing 3D scene structures from sparse, low-overlap observations remains a fundamental challenge in autonomous driving.
arXiv:2606. 10019v1 Announce Type: cross Abstract: We propose a fast and correspondence-free local point cloud registration method that leverages geometric surface structure and reproducing kernel Hilbert space (RKHS) embeddings.
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
arXiv:2605. 29987v2 Announce Type: replace Abstract: Although multi-scales representation learning enables elastic-dimension embeddings, nested subspaces often suffer from dimensional redundancy and spectral collapse.
arXiv:2606. 25347v1 Announce Type: new Abstract: Exemplar-free class-incremental learning (EFCIL) requires stable decision boundaries within a shifting feature space.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
Reconstructing 3D scenes from a single image is a fundamental challenge in computer vision, with broad applications in virtual reality, robotics, and content creation. Recent methods achieve outstanding performance by leveraging camera-controlled video diffusion models, but rely on iterative diffusion sampling, which greatly limits their practical deployment.
arXiv:2601. 23286v4 Announce Type: replace-cross Abstract: While recent video diffusion models (VDMs) produce visually impressive results, they fundamentally struggle to maintain 3D structural consistency, often resulting in object deformation or spatial drift.
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.