# Flow-Direct: Feedback-Efficient and Reusable Guidance for Flow Models via Non-Parametric Guidance Field

arXiv: https://arxiv.org/abs/2605.16348 · HTML: https://mlsanity.com/paper/2605.16348/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 23 of 23)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Structured 3D Latents for Scalable and Versatile 3D Generation](https://mlsanity.com/paper/2412.01506/) (2024)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models](https://mlsanity.com/paper/2402.17177/) (2024)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [A General Framework for Inference-time Scaling and Steering of Diffusion Models](https://mlsanity.com/paper/2501.06848/) (2025)
- [HPSv3: Towards Wide-Spectrum Human Preference Score](https://mlsanity.com/paper/2508.03789/) (2025)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [GenEval 2: Addressing Benchmark Drift in Text-to-Image Evaluation](https://mlsanity.com/paper/2512.16853/) (2025)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Dynamic Search for Inference-Time Alignment in Diffusion Models](https://mlsanity.com/paper/2503.02039/) (2025)
- [DoMINO: A Decomposable Multi-scale Iterative Neural Operator for Modeling Large Scale Engineering Simulations](https://mlsanity.com/paper/2501.13350/) (2025)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [Stochastic Sampling from Deterministic Flow Models](https://mlsanity.com/paper/2410.02217/) (2024)
- [Evolvable Conditional Diffusion](https://mlsanity.com/paper/2506.13834/) (2025)

## Abstract (arXiv)

Training-free guidance enables pre-trained diffusion and flow models to optimize application-specific objectives using feedback from external black-box reward functions. However, existing methods are feedback-inefficient because reward feedback is used only transiently to inform a localized gradient approximation or a discrete search decision, and is subsequently discarded. To address this limitation, we propose Flow-Direct, a framework that guides the generation process via a persistent guidance field. Theoretically, this guidance field is analytically derived from the log-density ratio between the base and reward-weighted target distributions; it transports the pre-trained distribution to the target distribution. In practice, the field is implemented as a non-parametric estimator constructed from all accumulated reward-evaluated samples. As more samples are collected during optimization, this empirical guidance field becomes increasingly accurate. This persistent formulation yields two major advantages. First, Flow-Direct is highly feedback-efficient: because every evaluated sample is used to refine the global guidance field, no reward information is wasted. Second, the framework is naturally reusable: once optimization is complete, the collected dataset defines a reusable guidance field for generating novel target samples without additional reward evaluations, and distinct guidance fields can be combined to generate samples that simultaneously satisfy multiple objectives.