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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.06800 |
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| _version_ | 1866918017352335360 |
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| author | Batista, Jairon H. N. Gonçalves, Flávio B. Saporito, Yuri F. Targino, Rodrigo S. |
| author_facet | Batista, Jairon H. N. Gonçalves, Flávio B. Saporito, Yuri F. Targino, Rodrigo S. |
| contents | Recently, there has been a growing interest in generative models based on diffusions driven by the empirical robustness of these methods in generating high-dimensional photorealistic images and the possibility of using the vast existing toolbox of stochastic differential equations. %This remarkable ability may stem from their capacity to model and generate multimodal distributions. In this work, we offer a novel perspective on the approach introduced in Song et al. (2021), shifting the focus from a "learning" problem to a "sampling" problem. To achieve this, we reformulate the equations governing diffusion-based generative models as a Forward-Backward Stochastic Differential Equation (FBSDE), which avoids the well-known issue of pre-estimating the gradient of the log target density. The solution of this FBSDE is proved to be unique using non-standard techniques. Additionally, we propose a numerical solution to this problem, leveraging on Deep Learning techniques. This reformulation opens new pathways for sampling multidimensional distributions with densities known up to a normalization constant, a problem frequently encountered in Bayesian statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reverse-BSDE Monte Carlo Batista, Jairon H. N. Gonçalves, Flávio B. Saporito, Yuri F. Targino, Rodrigo S. Machine Learning Probability Recently, there has been a growing interest in generative models based on diffusions driven by the empirical robustness of these methods in generating high-dimensional photorealistic images and the possibility of using the vast existing toolbox of stochastic differential equations. %This remarkable ability may stem from their capacity to model and generate multimodal distributions. In this work, we offer a novel perspective on the approach introduced in Song et al. (2021), shifting the focus from a "learning" problem to a "sampling" problem. To achieve this, we reformulate the equations governing diffusion-based generative models as a Forward-Backward Stochastic Differential Equation (FBSDE), which avoids the well-known issue of pre-estimating the gradient of the log target density. The solution of this FBSDE is proved to be unique using non-standard techniques. Additionally, we propose a numerical solution to this problem, leveraging on Deep Learning techniques. This reformulation opens new pathways for sampling multidimensional distributions with densities known up to a normalization constant, a problem frequently encountered in Bayesian statistics. |
| title | Reverse-BSDE Monte Carlo |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2505.06800 |