首次对离散时间生成模型进行有限时间分析，揭示收敛速度影响因素。
Finite-Time Analysis of Discrete-Time Stochastic Interpolants
- 提出新型离散时间采样器，突破连续时间假设限制。
- 推导出分布估计误差的有限时间上界，量化收敛速率。
- 为加速收敛提供可解释的调度设计方法，适合生成模型研究者。
随机插值框架为基于常微分方程（ODE）或随机微分方程（SDE）构建生成模型提供了强大工具，用于变换任意数据分布。然而，先前分析主要集中于连续时间设置，假设能精确求解底层方程。本文首次对随机插值框架进行离散时间分析，引入一种创新的离散时间采样器，并推导其分布估计误差的有限时间上界。该结果新颖地量化了源分布与目标分布间距离、估计精度等不同因素对收敛速率的影响，同时提供了一种新的、有理论依据的高效调度设计方法以加速收敛。最后，通过在离散时间采样器上的数值实验验证了理论发现。
原文摘要 · Abstract (English)
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions. However, prior analyses of this framework have primarily focused on the continuous-time setting, assuming a perfect solution of the underlying equations. In this work, we present the first discrete-time analysis of the stochastic interpolant framework, where we introduce an innovative discrete-time sampler and derive a finite-time upper bound on its distribution estimation error. Our result provides a novel quantification of how different factors, including the distance between source and target distributions and estimation accuracy, affect the convergence rate and also offers a new principled way to design efficient schedules for convergence acceleration. Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings.
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