Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary differential equations (ODE) rather than SDE. This led to the introduction of the probability flow ODE approach and denoising diffusion implicit models. Flow matching methods have recently further extended these ODE-based approaches and approximate a flow between two arbitrary probability distributions. Previous work derived bounds on the approximation error of diffusion models under the stochastic sampling regime, given assumptions on the $L^2$ loss. We present error bounds for the flow matching procedure using fully deterministic sampling, assuming an $L^2$ bound on the approximation error and a certain regularity condition on the data distributions.

翻译：基于分数的生成模型是一类依赖于随机微分方程的流行生成建模技术。从其诞生之初，人们就意识到，使用常微分方程而非随机微分方程也可以进行生成。这导致了概率流常微分方程方法和去噪扩散隐式模型的引入。流匹配方法最近进一步扩展了这些基于常微分方程的方法，并近似了两个任意概率分布之间的流。先前的工作在随机采样模式下，基于对$L^2$损失的假设，推导了扩散模型近似误差的界。我们针对完全确定性采样的流匹配过程，在假设近似误差的$L^2$界以及数据分布的特定正则性条件下，给出了误差界。