We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (i.e., denoising diffusion probabilistic modeling or DDPM), but requires the development of novel techniques for studying deterministic dynamics without contractivity. Through the use of a specially chosen corrector step based on the underdamped Langevin diffusion, we obtain better dimension dependence than prior works on DDPM ($O(\sqrt{d})$ vs. $O(d)$, assuming smoothness of the data distribution), highlighting potential advantages of the ODE framework.

翻译：我们首次为基于分数的生成模型中概率流ODE实现（结合校正步）提供了多项式时间收敛保证。本分析建立在近期为基于SDE的实现（即去噪扩散概率建模，DDPM）建立此类保证的研究基础之上，但需要针对无收缩性的确定性动力学开发新型分析技术。通过采用基于欠阻尼朗之万扩散的特殊校正步，我们在数据分布光滑性假设下获得了优于DDPM先前工作的维数依赖性（$O(\sqrt{d})$ vs. $O(d)$），凸显了ODE框架的潜在优势。