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Using a penalised maximum likelihood we estimate, for the first time, the velocity distribution of white dwarfs in the Solar neighbourhood. Our sample consists of 129 675 white dwarfs within 500 pc in Gaia Early Data Release 3 The white dwarf velocity distributions reveal a similar structure to the rest of the Solar neighbourhood stars, reflecting that white dwarfs are subjected to the same dynamical processes. In the velocity distribution for three magnitude-binned subsamples we however find a novel structure at $(U, V) = (7, -19)$ km s$^{-1}$ in fainter samples, potentially related to the Coma Berenices stream. We also see a double-peaked feature in $U$-$W$ at $U \approx -30$ km s$^{-1}$ and in $V$-$W$ at $V \approx -20$ km s$^{-1}$ for fainter samples. We determine the velocity distribution and velocity moments as a function of absolute magnitude for two samples based on the bifurcation identified in Gaia Data Release 2 in the colour-magnitude diagram. The brighter, redder sequence has a larger velocity dispersion than the fainter, bluer sequence across all magnitudes. It is hard to reconcile this kinematic difference with a bifurcation caused purely by atmospheric composition, while it fits neatly with a significant age difference between the two sequences. Our results provide novel insights into the kinematic properties of white dwarfs and demonstrate the power of analytical techniques that work for the large fraction of stars that do not have measured radial velocities in the current era of large-scale astrometric surveys., 18 pages, 10 figures. Accepted for publication in MNRAS