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Minimizing Trajectory Curvature of ODE-based Generative Models

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arxiv 2301.12003 v3 pith:NEDNIV5C submitted 2023-01-27 cs.LG cs.AIcs.CVstat.ML

Minimizing Trajectory Curvature of ODE-based Generative Models

classification cs.LG cs.AIcs.CVstat.ML
keywords curvaturegenerativemodelsprocessforwardmethodnumericalperformance
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 5 Pith papers

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