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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2605.19391 |
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| _version_ | 1866913144719278080 |
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| author | Tang, Wenpin Touzi, Nizar Zhang, Zikun Zhou, Xun Yu |
| author_facet | Tang, Wenpin Touzi, Nizar Zhang, Zikun Zhou, Xun Yu |
| contents | Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19391 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian Tang, Wenpin Touzi, Nizar Zhang, Zikun Zhou, Xun Yu Machine Learning Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models. |
| title | Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.19391 |