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We study the sensitivity to the Higgs trilinear self-coupling modifier κ₃ through VBF-induced di-Higgs production (HH → bbbb) at √s = 3 and 10 TeV muon colliders, with 1 and 10 ab⁻¹ of integrated luminosity, respectively. The analysis uses a two-stage machine learning pipeline: a symmetry-preserving attention network (SPANet) for jet-to-Higgs assignment, followed by two classifiers, one separating signal from background (ML1) and one discriminating between κ₃ hypotheses (ML2). Their outputs are combined in a two-dimensional binned likelihood to extract the κ₃ profile. The HH → bbbb final state is reconstructed in two complementary channels: a resolved four-jet topology and a boosted two-jet topology, which together cover the full Higgs pT spectrum. Combining the two channels, we obtain significantly tighter constraints on κ₃ compared to existing projections, demonstrating the strong potential of multi-TeV muon colliders for precision Higgs self-coupling measurements.