Score-based generative models (SGMs) aim at generating samples from a target distribution by approximating the reverse-time dynamics of a stochastic differential equation. Despite their strong empirical performance, classical samplers initialized from a Gaussian distribution require a long time horizon noising typically inducing a large number of discretization steps and high computational cost. In this work, we present a Kullback-Leibler convergence analysis of Variance Exploding diffusion samplers that highlights the critical role of the backward process initialization. Based on this result, we propose a theoretically grounded sampling strategy that learns the reverse-time initialization, directly minimizing the initialization error. The resulting procedure is independent of the specific score training procedure, network architecture, and discretization scheme. Experiments on toy distributions and benchmark datasets demonstrate competitive or improved generative quality while using significantly fewer sampling steps.

翻译：基于分数的生成模型旨在通过逼近随机微分方程的逆时动态，从目标分布中生成样本。尽管其经验性能优异，但传统采样器从高斯分布初始化通常需要较长的噪声化时间跨度，导致大量离散化步骤和高计算成本。本文针对方差爆炸扩散采样器提出了Kullback-Leibler收敛性分析，揭示了逆向过程初始化的关键作用。基于此分析，我们提出了一种理论依据充分的采样策略，通过学习逆向时间初始化直接最小化初始化误差。该流程独立于具体的分数训练方法、网络架构和离散化方案。在玩具分布和基准数据集上的实验表明，该方法在使用显著更少采样步数的同时，实现了具有竞争力或更优的生成质量。