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The paper proposes DiffTR, a diffusion-based method that learns a shared, coordinate-conditioned representation for tensor completion, denoising, and hyperspectral super-resolution without task-specific supervision. Its main contribution is separating representation learning from observation modeling, so one learned prior can be reused across corruption models. The reported results are described only as "competitive," so readers should check the benchmarks against established baselines before drawing conclusions.
Shared-Factor-Conditioned Diffusion for Low-Rank Tensor Recovery
arXiv:2610.35368v1 Announce Type: cross Abstract: Tensor recovery spans heterogeneous data structures and observation processes, calling for a representation that can adapt across modalities and tasks. We propose DiffTR, an unsupervised framework that unifies tensor completion, denoising, and hyperspectral super-resolution through coordinate-conditioned diffusion. Shared factors indexed by tensor coordinates condition a compact score network, and score matching jointly learns the factors and an implicit tensor representation from the available observations. Scalar and vector-valued outputs accommodate individual entries and entire tubes, enabling a common formulation for tabular tensors, images, and videos. The framework separates representation learning from task-specific observation modeling: reverse diffusion recovers missing values; estimation via Tweedie's formula, soft thresholding, and optional spatial consistency support mixed-noise denoising; and measurement-guided sampling transfers a prior learned from low-resolution hyperspectral observations to high-resolution reconstruction, followed by post-sampling refinement with data consistency and spectral subspace regularization. This separation makes the representation compatible with different corruption models and permits task-specific constraints to be incorporated within the same recovery framework. Experiments across multiple tensor modalities and recovery tasks demonstrate competitive reconstruction quality and the flexibility of a unified conditional generative representation. The code is available at https://github.com/CZY-Code/DiffTR
Abstract:Tensor recovery spans heterogeneous data structures and observation processes, calling for a representation that can adapt across modalities and tasks. We propose DiffTR, an unsupervised framework that unifies tensor completion, denoising, and hyperspectral super-resolution through coordinate-conditioned diffusion. Shared factors indexed by tensor coordinates condition a compact score network, and score matching jointly learns the factors and an implicit tensor representation from the available observations. Scalar and vector-valued outputs accommodate individual entries and entire tubes, enabling a common formulation for tabular tensors, images, and videos. The framework separates representation learning from task-specific observation modeling: reverse diffusion recovers missing values; estimation via Tweedie's formula, soft thresholding, and optional spatial consistency support mixed-noise denoising; and measurement-guided sampling transfers a prior learned from low-resolution hyperspectral observations to high-resolution reconstruction, followed by post-sampling refinement with data consistency and spectral subspace regularization. This separation makes the representation compatible with different corruption models and permits task-specific constraints to be incorporated within the same recovery framework. Experiments across multiple tensor modalities and recovery tasks demonstrate competitive reconstruction quality and the flexibility of a unified conditional generative representation. The code is available at this https URL
Computer Vision and Pattern Recognition (cs.CV); Artificial Intelligence (cs.AI)
arXiv:2610.35368 [cs.CV]
(or arXiv:2610.35368v1 [cs.CV] for this version)
https://doi.org/10.48550/arXiv.2610.35368 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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