Projected Energy Matching Slashes Compute for 3D Medical CT Reconstruction

A team led by Daniel Barco (arXiv:2607.07749) tackles a core bottleneck in generative 3D modeling: training energy-based models (EBMs) on high-dimensional data like medical CT scans. Standard energy matching distills pre-trained flow models but fails because velocity fields contain non-conservative rotational artifacts (curl). Forcing a scalar potential to match these fields creates structural conflicts, degrading generation quality and mode coverage.

The proposed Projected Energy Matching resolves this via two innovations. Helmholtz Distillation uses a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network, while Negative Caching reuses negative samples across micro-batches to make contrastive training tractable. Applied to sparse-view CT reconstruction, the method reduces total compute to a tiny fraction of prior energy matching, yields high-fidelity outputs, and eliminates severe measurement artifacts. The framework is amortized, making it practical for real-world inverse problems.