Potential Bug in SA Solver's Order 2 Modification

[superlanc3]

There seems to be a potential bug in the adams_bashforth_update_few_steps and adams_moulton_update_few_steps functions in RelaCtrl/diffusion/model/sa_solver.py when the order is set to 2. The added terms for the gradient coefficients modification might not be implemented correctly as the comments suggest they are for ODE case and the current implementation might not be fully compatible with the stochastic context.

Steps to Reproduce

1. Set the order parameter to 2 in the adams_bashforth_update_few_steps or adams_moulton_update_few_steps functions.
2. Run the sampling process.
3. Observe any unexpected behavior in the generated results.

Expected Behavior

The modification should improve the image quality without introducing any instability or incorrect results.

Actual Behavior

There might be instability or unexpected results in the generated images.

Possible Solution

Re - evaluate the implementation of the added terms for the gradient coefficients when order = 2 to ensure they are correct for the stochastic case.

[MaAo]

We appreciate your valuable suggestion. Admittedly, the issue you pointed out was not adequately addressed during our development process. For the time being, we suggest using the default order configuration. Further improvements to the code are planned for future iterations.