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We introduce and study a family of axioms that closely follows the pattern ofparametrized diamonds, studied by Moore, Hru\v{s}\'ak, and D\v{z}amonja in[13]. However, our approach appeals to model theoretic / forcing theoreticnotions, rather than pure combinatorics. The main goal of the paper is toexhibit a surprising, close connection between seemingly very distinctprinciples. As an application, we show that forcing with a measure algebrapreserves (a variant of) $\diamondsuit(\mathfrak{d})$, improving an old resultof M. Hru\v{s}\'ak.

Guessing genericity -- looking at parametrized diamonds from a different perspective