Topology-Conditioned Feasible-Set Generation for Continuous-Time Multigraphs

Generating temporal subgraphs requires changing interaction structure while preserving observations and quantitative constraints. Structural edits alter relay equations and can make pinned observations incompatible with positive flow. We formulate this as topology conditioned feasible-set generation. Each structural proposal induces its own constraint system, and the minimum distortion required to complete it shapes which structure is selected. A typed edit grammar and a policy trained to reconstruct corrupted skeletons propose and score admissible changes while protecting pinned events. A conditional diffusion prior then generates quantities and event times for each candidate topology. Each candidate is completed by Dirichlet-Boundary-Anchored KL projection (DBA-KL), which finds the closest positive flow that preserves pinned quantities and satisfies relay conservation. Under strict feasibility this completion is unique, and its KL distortion separates into the minimum change the constraints require plus any extra distortion from another feasible completion. All completed outputs preserve positive quantities and pinned observations, and every output containing a relay satisfies the relay-balance tolerance. On three anti-money-laundering benchmarks from a single simulator family, our DBA-KL configurations attain higher four-classifier average precision than the ECI-DBA and PCFM-log adaptations on all three. Relative gains reach 23.5% over ECI-DBA and 12.7% over PCFM-log on LI-Medium, and the terminal variant exceeds real-data training on HI-Small. Downstream accuracy alone is nevertheless a poor guide to constrained generation: an ablation that removes flow completion scores higher on every dataset while violating relay balance on 610 of 610 audited relay-containing outputs. Predictive utility and quantitative validity therefore have to be measured separately.