  Training-free guided sampling in diffusion models leverages off-the-shelf
pre-trained networks, such as an aesthetic evaluation model, to guide the
generation process. Current training-free guided sampling algorithms obtain the
guidance energy function based on a one-step estimate of the clean image.
However, since the off-the-shelf pre-trained networks are trained on clean
images, the one-step estimation procedure of the clean image may be inaccurate,
especially in the early stages of the generation process in diffusion models.
This causes the guidance in the early time steps to be inaccurate. To overcome
this problem, we propose Symplectic Adjoint Guidance (SAG), which calculates
the gradient guidance in two inner stages. Firstly, SAG estimates the clean
image via $n$ function calls, where $n$ serves as a flexible hyperparameter
that can be tailored to meet specific image quality requirements. Secondly, SAG
uses the symplectic adjoint method to obtain the gradients accurately and
efficiently in terms of the memory requirements. Extensive experiments
demonstrate that SAG generates images with higher qualities compared to the
baselines in both guided image and video generation tasks.
