Reverse-BSDE Monte Carlo

• URL: http://arxiv.org/abs/2505.06800v1
• Date: Sun, 11 May 2025 00:42:07 GMT
• Title: Reverse-BSDE Monte Carlo
• Authors: Jairon H. N. Batista, Flávio B. Gonçalves, Yuri F. Saporito, Rodrigo S. Targino,
• Abstract summary: We reformulate equations governing diffusion-based generative models as a Forward-Backward Differential Equation (FBSDE)<n>We propose a numerical solution to this problem, leveraging on Deep Learning techniques.
• Score: 1.8749305679160366
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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