One popular diffusion-based sampling strategy attempts to solve the reverse ordinary differential equations (ODEs) effectively. The coefficients of the obtained ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes by optimizing certain coefficients via improved integration approximation (IIA). At each reverse timestep, we propose to minimize a mean squared error (MSE) function with respect to certain selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps which in principle provides a more accurate integration approximation in predicting the next diffusion hidden state. Given a pre-trained diffusion model, the procedure for IIA for a particular number of neural functional evaluations (NFEs) only needs to be conducted once over a batch of samples. The obtained optimal solutions for those selected coefficients via minimum MSE (MMSE) can be restored and reused later on to accelerate the sampling process. Extensive experiments on EDM and DDIM show the IIA technique leads to significant performance gain when the numbers of NFEs are small.

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