A search is presented for a heavy resonance Y decaying into a Standard Model Higgs boson H and a new particle X in a fully hadronic final state. The full Large Hadron Collider run 2 dataset of proton-proton collisions at √s=13  TeV collected by the ATLAS detector from 2015 to 2018 is used and corresponds to an integrated luminosity of 139  fb−1. The search targets the high Y-mass region, where the H and X have a significant Lorentz boost in the laboratory frame. A novel application of anomaly detection is used to define a general signal region, where events are selected solely because of their incompatibility with a learned background-only model. It is constructed using a jet-level tagger for signal-model-independent selection of the boosted X particle, representing the first application of fully unsupervised machine learning to an ATLAS analysis. Two additional signal regions are implemented to target a benchmark X decay into two quarks, covering topologies where the X is reconstructed as either a single large-radius jet or two small-radius jets. The analysis selects Higgs boson decays into b¯b, and a dedicated neural-network-based tagger provides sensitivity to the boosted heavy-flavor topology. No significant excess of data over the expected background is observed, and the results are presented as upper limits on the production cross section σ(pp→Y→XH→q¯qb¯b) for signals with mY between 1.5 and 6 TeV and mX between 65 and 3000 GeV.