Elucidating Post-Training Conditioning in Pretrained Generative Flows

Conditional adaptation of pretrained generators has developed along seemingly distinct lines: some methods preserve the Gaussian source and add conditioning adapters or modules, bridges instead learn observation-centered transports from scratch, and recent work constructs such bridges from pretrained generators. We show that these approaches are parameterizations of a common post-training design space, determined by source information, explicit conditioning, and whether posterior randomness enters at the source or inside the transport. We then isolate the consequences of each choice. First, informative sources reduce the correction demanded of finite adapters, while vanishing source noise raises the expansion burden, producing a capacity–training crossover verified on GMMs and pretrained FLUX and SiT models. Second, source-noise ODEs and bridge-noise SDEs reach comparable conditional Energy, but require 4 and 64 evaluations, respectively. Third, with an informative source, removing the explicit condition arm largely preserves point fidelity despite a remaining posterior cost. These findings favor two practical recipes: an informative source-only ODE as the simplest efficient default, and a velocity-derived SDE that turns one source-only point-source checkpoint into both a deterministic restorer and an inference-time fidelity–diversity controller.