How to understand the linear noise schedule (Eq. 4) in paper?

[BlueGhostZ]

Notice that the author uses a new linear noise schedule instead of the Linear or cosine schedules used in DDPM. The selection in the code is noise_ schedule='linear var', which corresponds to lines 303-309 in gaussian_diffusion. py, but I do not understand the correspondence between these codes and Eq. 4 in the paper. I hope the author can help me.
Looking forward to your reply very much.

[YiyanXu]

The implementation of the linear noise schedule specified in Eq.(4) is represented by the np.linspace(...) operation found in line 53 of gaussian_diffusion.py. The function betas_from_linear_variance, which can be found in lines 303-309 of the same file, is responsible for deriving $\beta_t$ from the linear $1-\bar{\alpha}_t$.