A search for nonresonant Higgs boson (𝐻) pair production via gluon and vector boson (𝑉) fusion is performed in the four-bottom-quark final state, using proton-proton collision data at 13 TeV corresponding to 138  fb−1 collected by the CMS experiment at the LHC. The analysis targets Lorentz-boosted 𝐻 pairs identified using a graph neural network. It constrains the strengths relative to the standard model of the 𝐻 self-coupling and the quartic 𝑉⁢𝑉⁢𝐻⁡𝐻 couplings, 𝜅2⁢𝑉, excluding 𝜅2⁢𝑉 =0 for the first time, with a significance of 6.3 standard deviations when other 𝐻 couplings are fixed to their standard model values.