Train Separately, Compose at Sampling: Multi-Property Crystal Generation with Orthogonal Flow Guidance

Multi-property crystal generation is often bottlenecked by data: crystals satisfying multiple constraints jointly are rare, making it impractical to curate training sets or labels for $p(x\mid c_1,\ldots,c_m)$. We avoid this joint-data bottleneck by learning reusable, per-property guidance modules from single-property signals only. Starting from a pretrained unconditional base vector field, we fine-tune one flow model per property via an online, RL-style extension of Energy-Weighted Flow Matching (EWFM). Specifically, we sample trajectories from the current flow, score the resulting terminal crystals with fast property evaluators, and convert these scores into threshold-shaped importance weights to reweight the flow-matching objective. This yields property-specific correction fields without differentiable property gradients and any jointly labeled multi-property dataset. In inference, we satisfy new constraint sets by composing these fields (no retraining), and we reduce cross-objective interference by projecting each residual field to be orthogonal to the base flow before aggregation. On MP-20, composing stability and band-gap modules improves both objectives simultaneously: the formation-energy success rate increases from $0.754$ to $0.924$ (mean $-3.42 \rightarrow -4.35$ eV/atom), while the fraction with band gap $>3.0$ eV rises from $0.042$ to $0.157$ (mean $0.58 \rightarrow 1.19$ eV), with only a modest drop in diversity/coverage, validating that modular per-property fields can be composed to achieve multi-constraint generation without joint data or retraining.