Minimizing Trajectory Curvature of ODE-based Generative Models

Sangyun Lee, Beomsu Kim, Jong Chul Ye
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:18957-18973, 2023.

Abstract

Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-lee23j, title = {Minimizing Trajectory Curvature of {ODE}-based Generative Models}, author = {Lee, Sangyun and Kim, Beomsu and Ye, Jong Chul}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {18957--18973}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/lee23j/lee23j.pdf}, url = {https://proceedings.mlr.press/v202/lee23j.html}, abstract = {Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.} }
Endnote
%0 Conference Paper %T Minimizing Trajectory Curvature of ODE-based Generative Models %A Sangyun Lee %A Beomsu Kim %A Jong Chul Ye %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-lee23j %I PMLR %P 18957--18973 %U https://proceedings.mlr.press/v202/lee23j.html %V 202 %X Recent ODE/SDE-based generative models, such as diffusion models, rectified flows, and flow matching, define a generative process as a time reversal of a fixed forward process. Even though these models show impressive performance on large-scale datasets, numerical simulation requires multiple evaluations of a neural network, leading to a slow sampling speed. We attribute the reason to the high curvature of the learned generative trajectories, as it is directly related to the truncation error of a numerical solver. Based on the relationship between the forward process and the curvature, here we present an efficient method of training the forward process to minimize the curvature of generative trajectories without any ODE/SDE simulation. Experiments show that our method achieves a lower curvature than previous models and, therefore, decreased sampling costs while maintaining competitive performance. Code is available at https://github.com/sangyun884/fast-ode.
APA
Lee, S., Kim, B. & Ye, J.C.. (2023). Minimizing Trajectory Curvature of ODE-based Generative Models. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:18957-18973 Available from https://proceedings.mlr.press/v202/lee23j.html.

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