  We propose a scenario for the formation of DA white dwarfs with very thin
helium buffers. For these stars we explore the possible occurrence of
diffusion-induced CNO- flashes, during their early cooling stage. In order to
obtain very thin helium buffers, we simulate the formation of low mass remnants
through an AGB final/late thermal pulse (AFTP/LTP scenario). Then we calculate
the consequent white dwarf cooling evolution by means of a consistent treatment
of element diffusion and nuclear burning. Based on physically sounding white
dwarf models, we find that the range of helium buffer masses for these
diffusion-induced novas to occur is significantly smaller than that predicted
by the only previous study of this scenario. As a matter of fact, we find that
these flashes do occur only in some low-mass (M < 0.6M) and low metallicity
(Z_ZAMS <0.001) remnants about 10^6 - 10^7 yr after departing from the AGB. For
these objects, we expect the luminosity to increase by about 4 orders of
magnitude in less than a decade. We also show that diffusion-induced novas
should display a very typical eruption lightcurve, with an increase of about a
few magnitudes per year before reaching a maximum of M_V ~ -5 to -6. Our
simulations show that surface abundances after the outburst are characterized
by logNH/NHe ~ -0.15...0.6 and N>C>O by mass fractions. Contrary to previous
speculations we show that these events are not recurrent and do not change
substantially the final H-content of the cool (DA) white dwarf. (Abridged)
