Optimal Control Meets Flow Matching: A Principled Route to Multi-Subject
  Fidelity
Authors: name: Eric Tillmann Bill, name: Enis Simsar, name: Thomas Hofmann

Text-to-image (T2I) models excel on single-entity prompts but struggle with
multi-subject descriptions, often showing attribute leakage, identity
entanglement, and subject omissions. We introduce the first theoretical
framework with a principled, optimizable objective for steering sampling
dynamics toward multi-subject fidelity. Viewing flow matching (FM) through
stochastic optimal control (SOC), we formulate subject disentanglement as
control over a trained FM sampler. This yields two architecture-agnostic
algorithms: (i) a training-free test-time controller that perturbs the base
velocity with a single-pass update, and (ii) Adjoint Matching, a lightweight
fine-tuning rule that regresses a control network to a backward adjoint signal
while preserving base-model capabilities. The same formulation unifies prior
attention heuristics, extends to diffusion models via a flow-diffusion
correspondence, and provides the first fine-tuning route explicitly designed
for multi-subject fidelity. Empirically, on Stable Diffusion 3.5, FLUX, and
Stable Diffusion XL, both algorithms consistently improve multi-subject
alignment while maintaining base-model style. Test-time control runs
efficiently on commodity GPUs, and fine-tuned controllers trained on limited
prompts generalize to unseen ones. We further highlight FOCUS (Flow Optimal
Control for Unentangled Subjects), which achieves state-of-the-art
multi-subject fidelity across models.