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Improved Order Analysis and Design of Exponential Integrator for Diffusion Models Sampling by Zhang, Qinsheng; Song, Jiaming; Chen, Yongxin is a scholarly article available to read on EtoBox.

What is Improved Order Analysis and Design of Exponential Integrator for Diffusion Models Sampling about?

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers tha

Author

Zhang, Qinsheng; Song, Jiaming; Chen, Yongxin

Published

2023

Language

EN