A fresh attempt is made to clarify the physics of the diffuse, or spotless, mode of current transfer that may occur on cathodes of vacuum arcs if the average cathode surface temperature is high enough, about $2000 \operatorname {K}$ . It is shown that in the case of chromium cathode the usual mechanism of current transfer to arc cathodes cannot sustain current densities of the order of $10^{5}$ – $10^{6}~\operatorname {A}{\cdot }\operatorname {m}^{-2}$ observed in the experiment, the reason being that the electrical power deposited into electron gas in the near-cathode space-charge sheath is insufficient. It is hypothesized that the electrical power is supplied to the electron gas primarily in the bulk plasma, rather than in the sheath, and a high level of electron energy in the vicinity of the sheath edge is sustained by electron heat conduction from the bulk plasma. Estimates of the current of ions diffusing to the sheath edge from the quasi-neutral plasma gave values comparable with the experimental current density, which supports the above hypothesis. On the contrary, the spotless attachment of vacuum arcs to gadolinium cathodes may be interpreted as a manifestation of the usual mechanism of current transfer to arc cathodes. Results given for gadolinium cathodes by a model of near-cathode layers in vacuum arcs conform to available experimental information.