  Kobayashi recently proved that the generalized Heegner cycles of
Bertolini--Darmon--Prasanna can be interpolated along the anticyclotomic tower,
giving rise to distribution valued cohomology classes with expected growth
rate. We interpolate these classes along Coleman families. This construction
plays a role in the proofs of $p$-adic Gross--Zagier formulae at for
non-ordinary eigenforms and consequentially, also in the proof of a conjecture
of Perrin-Riou.
