  We present strong evidence that the broad, diffuse interstellar bands (DIBs)
at 4881 and 5450\,\AA are caused by the
$B\,^1$B$_1$\,$\leftarrow$\,$X\,^1$A$_1$ transition of H$_2$CCC (l-C$_3$H$_2$).
The large widths of the bands are due to the short lifetime of the $B\,^1$B$_1$
electronic state. The bands are predicted from absorption measurements in a
neon matrix and observed by cavity ring-down in the gas phase and show exact
matches to the profiles and wavelengths of the two broad DIBs. The strength of
the 5450\,\AA DIB leads to a l-C$_3$H$_2$ column density of
$\sim5\times10^{14}$ cm$^{-2}$ towards HD\,183143 and
$\sim2\times10^{14}$\,cm$^{-2}$ to HD\,206267. Despite similar values of
$E$($B-V$), the 4881 and 5450\,\AA DIBs in HD\,204827 are less than one third
their strength in HD\,183143, while the column density of interstellar C$_3$ is
unusually high for HD\,204827 but undetectable for HD\,183143. This can be
understood if C$_3$ has been depleted by hydrogenation to species such as
l-C$_3$H$_2$ towards HD\,183143. There are also three rotationally resolved
sets of triplets of l-C$_3$H$_2$ in the 6150$-$6330\,\AA region. Simulations,
based on the derived spectroscopic constants and convolved with the expected
instrumental and interstellar line broadening, show credible coincidences with
sharp, weak DIBs for the two observable sets of triplets. The region of the
third set is too obscured by the $\alpha$-band of telluric O$_2$.
