The implement of update equation of DPM in dpm_solver_pytorch.py is not same with the paper

[Yisten]

Hi, thank you for your excellent open-sourced work! I've been diving into the source code and came across something I’d appreciate some clarification on.

In dpm_solver_pytorch.py (lines 573–576), the update rule for x is:
'x_t = (
sigma_t / sigma_s * x
- alpha_t * phi_1 * model_s
)'

However according to DPM-solver, the update equation is:

I was wondering if there's a specific rationale behind such changes. Looking forward your reply, thank you!

[chaObserv]

The update you listed is the first order update of DPM-Solver++. The update equation for DPM-Solver can be found on lines 582–588.

[HuangJunJie2017]

The updation of dpm-slover-1 should be
x_t = ( torch.exp(log_alpha_t - log_alpha_s) * x - (sigma_t * (phi_1-1)) * model_s )
according to the updating equation in the paper.
why obmiting '-1' in 'phi_1-1'?

[HuangJunJie2017]

I got it, phi_1 is calculated by phi_1 = torch.expm1(-h), which has conducted calculation '-1' along with the exp calculation.

The updation of dpm-slover-1 should be x_t = ( torch.exp(log_alpha_t - log_alpha_s) * x - (sigma_t * (phi_1-1)) * model_s ) according to the updating equation in the paper. why obmiting '-1' in 'phi_1-1'?