Tucker Diffusion Model for High-dimensional Tensor Generation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| author | Guo, Jianhua Kong, Xinbing Li, Zeyu Mao, Junfan |
| author_facet | Guo, Jianhua Kong, Xinbing Li, Zeyu Mao, Junfan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tucker Diffusion Model for High-dimensional Tensor Generation Guo, Jianhua Kong, Xinbing Li, Zeyu Mao, Junfan Methodology Machine Learning 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. |
| title | Tucker Diffusion Model for High-dimensional Tensor Generation |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2604.00481 |