Oct 6, 2026, math.NAJ/K move · Enter open · S save
Christian Tantardini, Stig Rune Jensen, Roberto Di Remigio Eikås, Joakim Henrik Beck
Center for Integrative Petroleum Research, King Fahd University of Petroleum and Minerals, Dhahran 31261, Kingdom of Saudi Arabia · Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway · Algorithmiq S.r.l., c/o STLex, Via della Chiusa 15, 20123, Milano, Italia
Adaptive multiresolution methods reduce representation cost by concentrating fine-scale degrees of freedom where needed, but their tree updates are usually governed by fixed local criteria. We introduce Learned Adaptive Multiresolution Diffusion Imaging (Learned AMDI), which preserves the AMDI fixed-tree propagator and hierarchy constraints while replacing the post-propagation selector with a shared local policy trained by proximal policy optimization. Regression tests reproduce deterministic AMDI trajectories to machine precision when identical trees are used. In the Haar implementation studied here, the deterministic one-step selector accepts no refinements in 54 decisions. Across nine held-out cases, Learned AMDI executes 393 refinements and reduces the mean terminal reference discrepancy from
0.17496 to
0.13657, while occupancy rises from
0.13737 to
0.26660. Step-resolved diagnostics reveal occasional small adaptation-energy increases; fixed-tree energy stability therefore does not guarantee monotonicity of the learned outer iteration. At comparable occupancy, a validation-tuned observed-detail threshold reaches a discrepancy of
0.13792 with slightly better RMSE and SSIM, placing both methods on essentially the same accuracy--occupancy tradeoff. A decision-1-only control reaches
0.13742, indicating that most of the improvement on this static benchmark arises from the initial allocation. The shared actor transfers without retraining to
64×64 and
128×128 images, improving reference discrepancy, RMSE, and SSIM relative to deterministic AMDI, while the frozen threshold rule remains competitive. Learned AMDI thus provides a hierarchy-constrained, resolution-transferable mechanism for adaptive allocation and clarifies the contribution of sequential decisions.