Distributional Diffusion Models with Scoring Rules
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909676371705856 |
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| author | De Bortoli, Valentin Galashov, Alexandre Guntupalli, J. Swaroop Zhou, Guangyao Murphy, Kevin Gretton, Arthur Doucet, Arnaud |
| author_facet | De Bortoli, Valentin Galashov, Alexandre Guntupalli, J. Swaroop Zhou, Guangyao Murphy, Kevin Gretton, Arthur Doucet, Arnaud |
| contents | Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises" a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {\em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributional Diffusion Models with Scoring Rules De Bortoli, Valentin Galashov, Alexandre Guntupalli, J. Swaroop Zhou, Guangyao Murphy, Kevin Gretton, Arthur Doucet, Arnaud Machine Learning Diffusion models generate high-quality synthetic data. They operate by defining a continuous-time forward process which gradually adds Gaussian noise to data until fully corrupted. The corresponding reverse process progressively "denoises" a Gaussian sample into a sample from the data distribution. However, generating high-quality outputs requires many discretization steps to obtain a faithful approximation of the reverse process. This is expensive and has motivated the development of many acceleration methods. We propose to accomplish sample generation by learning the posterior {\em distribution} of clean data samples given their noisy versions, instead of only the mean of this distribution. This allows us to sample from the probability transitions of the reverse process on a coarse time scale, significantly accelerating inference with minimal degradation of the quality of the output. This is accomplished by replacing the standard regression loss used to estimate conditional means with a scoring rule. We validate our method on image and robot trajectory generation, where we consistently outperform standard diffusion models at few discretization steps. |
| title | Distributional Diffusion Models with Scoring Rules |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.02483 |