Bayesian computation with generative diffusion models by Multilevel Monte Carlo
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908362768121856 |
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| author | Haji-Ali, Abdul-Lateef Pereyra, Marcelo Shaw, Luke Zygalakis, Konstantinos |
| author_facet | Haji-Ali, Abdul-Lateef Pereyra, Marcelo Shaw, Luke Zygalakis, Konstantinos |
| contents | Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion models often require a large number of neural function evaluations per sample in order to deliver accurate posterior samples. As a result, using diffusion models as stochastic samplers for Monte Carlo integration in Bayesian computation can be highly computationally expensive, particularly in applications that require a substantial number of Monte Carlo samples for conducting uncertainty quantification analyses. This cost is especially high in large-scale inverse problems such as computational imaging, which rely on large neural networks that are expensive to evaluate. With quantitative imaging applications in mind, this paper presents a Multilevel Monte Carlo strategy that significantly reduces the cost of Bayesian computation with diffusion models. This is achieved by exploiting cost-accuracy trade-offs inherent to diffusion models to carefully couple models of different levels of accuracy in a manner that significantly reduces the overall cost of the calculation, without reducing the final accuracy. The proposed approach achieves a $4\times$-to-$8\times$ reduction in computational cost w.r.t. standard techniques across three benchmark imaging problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bayesian computation with generative diffusion models by Multilevel Monte Carlo Haji-Ali, Abdul-Lateef Pereyra, Marcelo Shaw, Luke Zygalakis, Konstantinos Computation Computer Vision and Pattern Recognition Machine Learning Generative diffusion models have recently emerged as a powerful strategy to perform stochastic sampling in Bayesian inverse problems, delivering remarkably accurate solutions for a wide range of challenging applications. However, diffusion models often require a large number of neural function evaluations per sample in order to deliver accurate posterior samples. As a result, using diffusion models as stochastic samplers for Monte Carlo integration in Bayesian computation can be highly computationally expensive, particularly in applications that require a substantial number of Monte Carlo samples for conducting uncertainty quantification analyses. This cost is especially high in large-scale inverse problems such as computational imaging, which rely on large neural networks that are expensive to evaluate. With quantitative imaging applications in mind, this paper presents a Multilevel Monte Carlo strategy that significantly reduces the cost of Bayesian computation with diffusion models. This is achieved by exploiting cost-accuracy trade-offs inherent to diffusion models to carefully couple models of different levels of accuracy in a manner that significantly reduces the overall cost of the calculation, without reducing the final accuracy. The proposed approach achieves a $4\times$-to-$8\times$ reduction in computational cost w.r.t. standard techniques across three benchmark imaging problems. |
| title | Bayesian computation with generative diffusion models by Multilevel Monte Carlo |
| topic | Computation Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2409.15511 |