Tucker Diffusion Model for High-dimensional Tensor Generation

• URL: http://arxiv.org/abs/2604.00481v1
• Date: Wed, 01 Apr 2026 04:55:18 GMT
• Title: Tucker Diffusion Model for High-dimensional Tensor Generation
• Abstract summary: We propose a novel Tucker diffusion model for learning high-dimensional tensor distributions.<n>We show that the score function admits a structured decomposition under the low Tucker rank assumption, allowing it to be both accurately approximated and efficiently estimated.<n>The distribution of generated tensors, induced by the estimated score function, converges to the true data distribution at a rate depending on the maximum of tensor mode dimensions.
• Score: 4.003168383221301
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target distribution is still a new problem. As profound AI generators, diffusion models have achieved remarkable success in learning complex distributions. However, their extension to generating multi-linear tensor-valued observations remains underexplored. In this work, we propose a novel Tucker diffusion model for learning high-dimensional tensor distributions. We show that the score function admits a structured decomposition under the low Tucker rank assumption, allowing it to be both accurately approximated and efficiently estimated using a carefully tailored tensor-shaped architecture named Tucker-Unet. Furthermore, the distribution of generated tensors, induced by the estimated score function, converges to the true data distribution at a rate depending on the maximum of tensor mode dimensions, thereby offering a clear theoretical advantage over the naive vectorized approach, which has a product dependence. Empirically, compared to existing approaches, the Tucker diffusion model demonstrates strong practical potential in synthetic and real-world tensor generation tasks, achieving comparable and sometimes even superior statistical performance with significantly reduced training and sampling costs.

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