In this work we introduced DPP-BBO, a natural and easily applicable framework for enhancing batch diversity in BBO algorithms which works in more settings than previous diversification strategies: it is directly applicable to the continuous domain case, when due to approximation and non-standard models we are unable to compute hallucinations or confidence intervals (as in the Cox process example), or more generally when used in combination with any randomized BBO sampling scheme or arbitrary diversity kernel. Moreover, for DPP-TS we show improved theoretical guarantees and strong practical performance on simple regret.