  The search for double Higgs production in $b\bar{b}W^+W^-$, where both $W$
bosons decay to leptons, has been rehabilitated as a good option to look for
that key process to the Standard Model scalar sector study in the LHC. The
missing neutrinos, however, hinder the reconstruction of useful information
like the Higgs pair mass, which is very sensitive to the trilinear Higgs
self-coupling. We present a solution to that problem using a Variational
Autoencoder for Regression (VAER) to reconstruct the Higgs and top pairs decays
$hh,t\bar{t}\to b\bar{b}W^+W^-\to b\bar{b}\ell^+\ell^{\prime
-}\nu_\ell\bar{\nu}_{\ell^\prime}$. The algorithm predicts the invariant mass
of non-resonant $hh$ irrespective of the trilinear coupling, even for events
whose Higgs self-couplings were never presented to it. VAER is also able to
identify a new Higgs resonance in an unsupervised way, showing generalization
power for events not presented in its training phase. Finally, we demonstrate
that VAER prediction is as useful to statistical inference as ground truth
simulated distributions by computing a $\chi^2$ between trilinear coupling
hypotheses based on binned invariant mass distributions of
$b\bar{b}\ell^+\ell^{\prime -}\nu_\ell\bar{\nu}_{\ell^\prime}$.
