Why does the approximate equality in Eq.(24) holds?

[chenweize1998]

Hi! When I'm reading the proof that DDPM is a discretization of the VP-SDE in Appendix B of https://openreview.net/pdf?id=PxTIG12RRHS, I don't understand why Eq.(24) holds. I know that when $x\ll 1, \sqrt{1-x} \approx 1-x/2$. However, In Eq.(24), $\beta(t+\Delta t)\Delta t$ seems to not satisfy this condition, because $\beta(t)=N\beta_i$, and when $\Delta t\rightarrow 0, N\rightarrow \infty$. Could you explain why this approximate equality still holds?