Questions about infenerce

[zhuhui-in]

1. in the inference procedure, the ligand pose was noised according to $$\theta_N ~ Uni(SO(2)^m), R_n ~ Uni(SO(3)), r_N ~ N(0,\sigma_{tor}^2(T))$$, why not is the same as sampling from diffusion kernels as training procedure?
2. The denoise process is a little different between the pseudocode in the paper and the code in the GitHub in paper it was $$r_{n-1} \gets r_n + \Delta\sigma_{tr}^2\alpha + z_{tr}$$ in the GitHub code it is: tr_perturb = (tr_g ** 2 * dt_tr * tr_score.cpu() + tr_g * np.sqrt(dt_tr) * tr_z).cpu(), which means $$r_{n-1} \gets r_n + g(t)^2 \Delta\sigma_{tr}^2\alpha + g(t) z_{tr}$$ the reverse SDE was $$dx=-g(t)^2 s_\theta(x,t)dt + g(t)dw$$ would you please me better understanding the relationship among three?