Discriminant Flow Steering: Training-Free Capability Transfer in Flow-Matching Models

Open flow-matching image models fail specific, checkable and sometimes trivial capabilities that stronger, often closed, models handle like a three-column menu, an orthographic drawing, or a diagram with exactly three boxes. We ask whether we can close such a gap with no training, no teacher weights and no teacher call at inference, and from about twenty images from each model. To answer this, we propose Discriminant Flow Steering (DFS), which encodes the teacher images with the student’s VAE and uses the difference between the mean teacher latent and the mean student latent as the steering direction when generating new images. The unit vector along this difference is added to the latent during the first sampling steps; nothing else changes. We find that this vector is what guidance with a second model adds at each step, except that we compute it only once and offline. This holds exactly at the first step for any two models, and approximately at high noise if we model the latents as Gaussian. Prior steering methods fit their direction at the same noise level where they apply it. We derive the exact finite-sample law for such a fit and find that, in the first steps where steering matters most, 99% of the fitted direction is noise. This is why we estimate the direction from clean latents. We also measure how far a perturbation injected at each step travels to the final image. At the first step the mean difference is amplified 8.8 times more than a random direction, and by mid-trajectory the advantage is gone. To measure capability transfer rather than resemblance to the teacher, we build DFS-CapBench: 200 prompts in 20 capability families, each with a frozen checklist, admitted only if the teacher passes and the student fails. An open vision-language model judges every checklist item and never sees a teacher image. On the 126 strict prompts DFS passes 42.1% of images at one global strength, against 10.1% for the student on fresh seeds, and above prompt rewriting, guidance sweeps and negative-prompt guidance with the same access. Attention-space negative guidance does better than DFS when the failure can be named in a negative prompt, and worse when the missing capability is structural, so the two methods complement each other. When we combine them, they pass 63.9% of images, on par with a per-prompt LoRA trained on the same images. On structural capabilities DFS alone passes more images than that LoRA and keeps the student’s seed diversity. We also test the same method on a second student, a second teacher, and a small-scale video experiment.