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（SDE）的流行生成建模技术。自其诞生之初，人们便认识到使用常微分方程（ODE）而非SDE进行生成也是可行的。这促使了概率流ODE方法和去噪扩散隐式模型的提出。流匹配方法近期进一步扩展了这些基于ODE的方法，并近似任意两个概率分布之间的流。先前的研究在随机采样机制下，基于对$L^2$损失的假设，推导了扩散模型近似误差的界。我们则提出了在完全确定性采样条件下，流匹配过程的误差界，该界假设近似误差具有$L^2$界，且数据分布满足一定的正则性条件。