Issues Integrating SuperDiff with Flow Matching Algorithm and other Beta Schedule Methods

[SageCao1125]

Thanks for your amazing work!

I am currently working on integrating the SuperDiff algorithm with the Flow Matching algorithm. Based on the tutorial for SD Superposition_AND & OR, I observed that the get_vel function always predicts epsilon, which is then used to calculate kappa based on the bg & obj's epsilon.

However, if I want to use a model based on FlowMatchEulerDiscreteScheduler, which predicts v=epsilon-x0, I need to align this with the approach provided by SuperDiff that uses epsilon to compute kappa.

To achieve this, I modified the code to use the relationship: xt = sigma*epsilon + (1-sigma)*x0 and v=epsilon-x0.
Then, I derive the predicted epsilon from Flow Matching as: epsilon=xt+(1-sigma)*v.

Using this adjusted epsilon, I proceed with the subsequent kappa calculation. However, I encountered a problem: during the first step, when sigma=1, the kappa becomes NaN. After clipping the values, the results remain significantly poor.

Therefore, I have the following questions:

1. Does the kappa calculation in the provided SuperDiff code apply only to diffusion-based models with prediction_type=epsilon ? (I believe this is not inherently the case, but I am uncertain if the code needs to be adjusted.)
2. For a model trained with FlowMatchEulerDiscreteScheduler, which predicts v=epsilon-x0, how can I compute kappa using SuperDiff? Where might my approach be flawed?
3. Why does the solution in the code correspond to solving a linear equation in theory? I perceive a gap between the code and the theoretical formulation.

I would greatly appreciate any insights or guidance!

Thanks!

[SageCao1125]

Another question is:

How can superdiff be adapted to other beta_schedule methods?

In my experiment, I found that superdiff performs well with diffusion models trained with beta_schedule = 'scaled_linear', but performs very poorly with beta_schedule = 'squaredcos_cap_v2'. Do authors have any suggestions for this?

Thanks!