DDIMInverseScheduler.step: Incorrect Previous Timestep Calculation

[stop1one]

Describe the bug

There is a bug in DDIMInverseScheduler.step related to how the previous timestep is computed.
The inverse scheduler should move from timestep $t+1$ to $t$, but currently, the code is mistakenly computing $t-1$ instead of $t+1$.
https://github.com/huggingface/diffusers/blob/89e4d6219805975bd7d253a267e1951badc9f1c0/src/diffusers/schedulers/scheduling_ddim_inverse.py#L327C1-L331C10

This should be corrected to ensure the inverse process aligns properly with the intended scheduling.

# 1. get previous step value (=t+1)
prev_timestep = min(
    timestep + self.config.num_train_timesteps // self.num_inference_steps, 
    self.config.num_train_timesteps - 1
)

For comparison, DDIMScheduler correctly calculates $t-1$, as expected in a forward process:
https://github.com/huggingface/diffusers/blob/89e4d6219805975bd7d253a267e1951badc9f1c0/src/diffusers/schedulers/scheduling_ddim.py#L401C1-L402C95

Reproduction

This issue is straightforward to verify, so a reproduction snippet is omitted.

Logs

System Info

diffusers==0.32.2

Who can help?

@yiyixuxu

[github-actions]

This issue has been automatically marked as stale because it has not had recent activity. If you think this still needs to be addressed please comment on this thread.

Please note that issues that do not follow the contributing guidelines are likely to be ignored.

[andreabosisio]

I'm also a bit confused about this implementation (and of the inversion formulas in general), also because of this bug #10920. Also, I don't understand why previous timestep is t+1 here

diffusers/src/diffusers/schedulers/scheduling_ddim_inverse.py

Line 327 in 89e4d62

# 1. get previous step value (=t+1)

However, I believe the change you proposed may not be correct, as at timestep=0, you would need to compute the alpha coefficients for that specific timestep, whereas with your suggested change, alpha_prod_t = self.alphas_cumprod[timestep] would use the alpha coefficients for the next DDIM timestep, which would be inaccurate.

Additionally, after testing it on my model, it appears that the noising process fails with your modifications: x_t remains unchanged throughout the process and stays as the initial input x_0 .