用正向-反向随机微分方程统一采样过程，提升复杂分布生成效果。
A Reverse-BSDE Diffusion Sampler
- 将逆时扩散采样重构为耦合的前向-后向随机微分方程
- 在香蕉形和环形分布上生成质量优于传统方法
- 适合处理全局结构复杂的高维分布建模
基于扩散的生成模型重新引发了对随机微分方程采样方法的关注。本文研究目标密度仅知归一化常数的情况，将逆时扩散采样重构为前向-后向随机微分方程（FBSDE）。该形式取代了对时变得分函数的独立预估计，转而求解一个耦合随机系统。我们证明了两种形式的等价性，并给出了因初始化标准高斯、欧拉离散化动态过程以及近似求解FBSDE所导致的近似误差分解。我们在合成目标上评估了该算法，包括分离混合分布、各向异性高斯分布、香蕉形和环形分布。结果表明该方法在具有复杂全局结构的目标上表现优异。
原文摘要 · Abstract (English)
Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions. We study a setting in which the target density is known only up to a normalizing constant and reformulate the reverse-time diffusion sampler as a forward-backward stochastic differential equation (FBSDE). This formulation replaces the separate pre-estimation of the time-dependent score with the solution of a coupled stochastic system. We prove the equivalence of these formulations and provide a decomposition of the approximation error arising from initializing the sampler with a standard Gaussian, applying Euler discretization to the dynamics, and solving the FBSDE approximately. We then evaluate the proposed algorithm on synthetic targets, including separated mixtures, anisotropic Gaussian distributions, and banana-shaped and ring-shaped distributions. The results demonstrate the promise of the method, particularly for targets with complex global structure.
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