Title: Integrating Diffusion Model Priors into Bayesian Tensor Decomposition

Abstract: While low-rank tensor decomposition (TD) performs well on complete, noise-free datasets, its efficacy typically diminishes when faced with significant missing data or corruption. Although low-rankness serves as a valuable structural prior, it is inherently limited; supplementary handcrafted constraints, such as smoothness or sparsity, often fail to adequately model the complex statistics inherent in real-world data. To overcome the weak inductive bias associated with heavy corruption, it is desirable to incorporate a learned, data-driven prior. However, integrating state-of-the-art diffusion models into existing TD frameworks and performing tractable posterior inference remains a significant challenge.

To resolve these issues, we propose DiffBCP, a hybrid-prior Bayesian CP decomposition framework. This approach combines a cumulative shrinkage process prior over CP factors to facilitate automatic rank selection with an off-the-shelf, pre-trained diffusion model that acts as an implicit data prior for the reconstructed tensor. Despite the complex interplay between the likelihood function, low-rank constraints, and the diffusion prior, we ensure tractable posterior inference by developing a split Gibbs sampler. Within this sampler, CP factors are updated using conjugate methods, while the diffusion component is sampled through low-rank-guided denoising. Additionally, a noise-adaptive coupling schedule is employed to minimize sensitivity to manually tuned annealing parameters. Empirical evaluations on image inpainting and denoising tasks, including high-resolution out-of-distribution images, demonstrate consistent improvements over baselines based on Bayesian, nonlinear, and plug-and-play TD methods.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC