We give the first examples of products of finitely axiomatisable modal logics that are not finitely axiomatisable but axiomatisable by explicit infinite sets of canonical (sometimes even Sahlqvist) axioms. In particular, we study here modal products with Diff, the propositional unimodal logic of the difference operator. We show that the 2D product logic Diff× Diff is non-finitely axiomatisable, but can be axiomatised by infinitely many Sahlqvist axioms. We also show that its ‘square’version Diff× sq Diff (the modal counterpart of two-variable substitution and equality free first-order logic with counting to 2) is non-finitely axiomatisable over Diff× Diff, but can be axiomatised by adding infinitely many canonical axioms.