Follow the Mean: Reference-Guided Flow Matching

• URL: http://arxiv.org/abs/2605.10302v2
• Date: Tue, 12 May 2026 09:36:29 GMT
• Title: Follow the Mean: Reference-Guided Flow Matching
• Abstract summary: We show that flow matching admits a different control interface: adaptation through examples.<n>For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself.<n>This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows.
• Score: 10.73543578064991
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.

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