Title: Steering Generation with Precision: A Minimal-Step Alignment Method Using Flow Map Reward Guidance

Abstract: A central challenge in generative modeling is guidance—the process of generating samples that optimize a specific user-defined objective, such as adhering to human preferences or achieving high aesthetic standards. Current techniques for this task are often limited by their reliance on computationally intensive, multi-particle, multi-step procedures or on approximations whose theoretical underpinnings remain unclear. To address these limitations, we recast the guidance problem as a deterministic optimal control problem. This reformulation produces a spectrum of algorithms that encompasses existing methods as their coarsest approximation. Our analysis reveals that the flow map, a structure recently highlighted for enabling rapid inference, emerges organically within the optimal solution. Leveraging this insight, we introduce Flow Map Reward Guidance (FMRG), a novel framework that is training-free and operates via a single trajectory. By utilizing the flow map for both integration and guidance, FMRG achieves performance comparable to or better than baseline methods in both inverse problems and reward-driven generation at text-to-image scales. Notably, it accomplishes this with as few as 3 NFEs, delivering a speed improvement of at least one order of magnitude over current state-of-the-art approaches. The source code can be accessed at https://github.com/jrrhuang/fmrg.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC