{"ID":6267496,"CreatedAt":"2026-07-10T01:11:38.759438437Z","UpdatedAt":"2026-07-11T10:22:07.798851522Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.07749","arxiv_id":"2607.07749","title":"Projected Energy Matching for Generative 3D Priors","abstract":"Energy Matching has emerged as a powerful generative framework that combines flow model efficiency with the explicit likelihood of Energy-Based Models (EBMs) via a single, time-independent scalar potential. However, directly training this potential on high-dimensional 3D data remains computationally challenging. While distilling a pre-trained flow model circumvents some of the initial training costs, we demonstrate that velocity fields inevitably contain non-conservative rotational artifacts (curl). Forcing a strictly conservative scalar potential to match this unconstrained field creates a \"structural conflict\", which degrades generation quality and mode coverage. To solve this, we propose Projected Energy Matching, a scalable framework that resolves these structural and computational bottlenecks. We introduce Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network. We subsequently refine this landscape using Negative Caching, a memory-efficient strategy that reuses negative samples across micro-batches, rendering sampling tractable during contrastive training with gradient accumulation. We deploy our method as an unconditional prior for real-world medical CT inverse problems, specifically sparse-view reconstruction. Ultimately, our amortized pipeline reduces total compute to a small fraction of that required by standard energy matching, while achieving high-fidelity reconstructions and successfully resolving severe measurement artifacts.","short_abstract":"Energy Matching has emerged as a powerful generative framework that combines flow model efficiency with the explicit likelihood of Energy-Based Models (EBMs) via a single, time-independent scalar potential. However, directly training this potential on high-dimensional 3D data remains computationally challenging. While...","url_abs":"https://arxiv.org/abs/2607.07749","url_pdf":"https://arxiv.org/pdf/2607.07749v1","authors":"[\"Daniel Barco\",\"Michal Balcerak\",\"Suprosanna Shit\",\"Chinmay Prabhakar\",\"Philipp Denzel\",\"Bjoern Menze\",\"Frank-Peter Schilling\"]","published":"2026-07-08T10:25:21Z","proceeding":"eess.IV","tasks":"[\"eess.IV\",\"q-bio.QM\"]","methods":"[]","has_code":false}