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We study the fraction of the intra-cluster light (ICL) formed in-situ in the three most massive clusters of the TNG50 simulation, with virial masses $\sim {10}^{14}$. We find that a significant fraction of ICL stars ( $8\%$- $28\%$) are born in-situ. This amounts to a total stellar mass comparable to the central galaxy itself. Contrary to simple expectations, only a sub-dominant fraction of these in-situ ICL stars are born in the central regions and later re-distributed to more energetic orbits during mergers. Instead, many in-situ ICL stars form directly hundreds of kiloparsecs away from the central galaxy, in clouds condensing out of the circum-cluster medium. The simulations predict a present-date diffuse star formation rate of $$1 ${\mathrm{M}}_{\odot }$/yr, with higher rates at higher redshifts. The diffuse star forming component of the ICL is filamentary in nature, extends for hundreds of kiloparsecs and traces the distribution of neutral gas in the cluster host halo. We discuss briefly how numerical details of the baryonic treatment in the simulation, in particular the density threshold for star formation and the equation of state, may play a role in this result. We conclude that a sensitivity of $1.6\times {10}^{-19}-2.6\times {10}^{-18}$erg s ${}^{-1}$cm ${}^{-2}$arcsec ${}^{-2}$in H ${}_{\alpha }$flux (beyond current observational capabilities) would be necessary to detect this diffuse star-forming component in galaxy clusters.