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\title{The probability flow ODE is provably fast}


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\author{%
Sitan Chen\thanks{Harvard University, \url{sitan@seas.harvard.edu}} \\
\And 
Sinho Chewi\thanks{Institute for Advanced Study, \url{schewi@ias.edu}} \\
\And Holden Lee\thanks{Johns Hopkins University, \url{hlee283@jhu.edu}} \\
\And Yuanzhi Li\thanks{Microsoft Research, \url{yuanzhili@microsoft.com}} \\
\And Jianfeng Lu\thanks{Duke University, \url{jianfeng@math.duke.edu}} \\
\And Adil Salim\thanks{Microsoft Research, \url{adilsalim@microsoft.com}} \\
  % David S.~Hippocampus\thanks{Use footnote for providing further information
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  % Department of Computer Science\\
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\begin{document}


\maketitle


\begin{abstract}
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling \edit{with an OU forward process}.
Our analysis is carried out in the wake of recent results obtaining such guarantees for the SDE-based implementation (\emph{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.
\end{abstract}

\input{intro}
\input{prelim}
\input{results}
\input{sketch}
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\input{conclusion}
\printbibliography{}
\appendix
\newpage
\input{overview}
\input{score_perturbation}
\input{predictor}
\input{corrector}
\input{end-to-end}
\input{experiments}

\end{document}