{"ID":2861663,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.02315","arxiv_id":"2510.02315","title":"FOCUS: Optimal Control for Multi-Entity World Modeling in Text-to-Image Generation","abstract":"Text-to-image (T2I) models excel on single-entity prompts but struggle with multi-entity scenes, often exhibiting attribute leakage, identity entanglement, and subject omissions. We present a principled theoretical framework that steers sampling toward multi-subject fidelity by casting flow matching (FM) as stochastic optimal control (SOC), yielding a single hyperparameter controlled trade-off between fidelity and object-centric state separation / binding consistency. Within this framework, we derive 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. 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. In addition, we also introduce FOCUS (Flow Optimal Control for Unentangled Subjects), a probabilistic attention-binding objective compatible with both algorithms. Empirically, on Stable Diffusion 3.5 and FLUX.1, both algorithms consistently improve multi-subject alignment while maintaining base-model style; test-time control runs efficiently on commodity GPUs, and fine-tuned models generalize to unseen prompts.","short_abstract":"Text-to-image (T2I) models excel on single-entity prompts but struggle with multi-entity scenes, often exhibiting attribute leakage, identity entanglement, and subject omissions. We present a principled theoretical framework that steers sampling toward multi-subject fidelity by casting flow matching (FM) as stochastic...","url_abs":"https://arxiv.org/abs/2510.02315","url_pdf":"https://arxiv.org/pdf/2510.02315v2","authors":"[\"Eric Tillmann Bill\",\"Enis Simsar\",\"Thomas Hofmann\"]","published":"2025-10-02T17:59:58Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[\"Diffusion Model\"]","has_code":false}