Compositional Energy-Based Inference-Time Scaling for Multi-Scale Microstructure Generation

Generating scale-consistent scientific images requires satisfying physical constraints over combinatorial conditions, while standard point-wise selection can collapse the joint distribution. We introduce Compositional Energy-Based Scaling (CEBS), an inference-time scaling framework based on compositional energy minimization. CEBS decomposes a jointly trained conditional diffusion model into condition-specific energy gradients and recombines them for controllable out-of-distribution generation without retraining. It further defines a set-level energy that penalizes mean shift and covariance mismatch, selecting candidate subsets that preserve distributional statistics rather than optimizing samples independently. CEBS is general to conditional generators, requires no auxiliary discriminator, and improves scientific image generation under interpretable statistical and physical constraints.